var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"http://www.cs.columbia.edu/~ccanonne/tutorial-focs2020/publications-annotated.bib\",\"fullnames\":\"1\",\"sort\":\"title\",\"theme\":\"dividers\",\"jsonp\":\"1\",\"folding\":\"0\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"A General Characterization of the Statistical Query Complexity\",\"author\":[{\"firstnames\":[\"Vitaly\"],\"propositions\":[],\"lastnames\":[\"Feldman\"],\"suffixes\":[]}],\"pages\":\"785–830\",\"year\":\"2017\",\"editor\":[{\"firstnames\":[\"Satyen\"],\"propositions\":[],\"lastnames\":[\"Kale\"],\"suffixes\":[]},{\"firstnames\":[\"Ohad\"],\"propositions\":[],\"lastnames\":[\"Shamir\"],\"suffixes\":[]}],\"volume\":\"65\",\"series\":\"Proceedings of Machine Learning Research\",\"address\":\"Amsterdam, Netherlands\",\"month\":\"07–10 Jul\",\"publisher\":\"PMLR\",\"pdf\":\"http://proceedings.mlr.press/v65/feldman17c/feldman17c.pdf\",\"url\":\"http://proceedings.mlr.press/v65/feldman17c.html\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[Feldman17]</span> Provides a characterization of SQ learning in terms of new \\\"statistical dimension;\\\" to be seen in view of the poly-factor equivalence between SQ learning and LDP-constrained/memory-constrained learnin (e.g., [KLNRS11,BDD98]). Includes applications to memory-limited streaming and communication-limited learning.</div>\",\"bibtex\":\"@inproceedings{Feldman17,\\n  title = \\t {A General Characterization of the Statistical Query Complexity},\\n  author = \\t {Vitaly Feldman},\\n  pages = \\t {785--830},\\n  year = \\t {2017},\\n  editor = \\t {Satyen Kale and Ohad Shamir},\\n  volume = \\t {65},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  address = \\t {Amsterdam, Netherlands},\\n  month = \\t {07--10 Jul},\\n  publisher =    {PMLR},\\n  pdf = \\t {http://proceedings.mlr.press/v65/feldman17c/feldman17c.pdf},\\n  url = \\t {http://proceedings.mlr.press/v65/feldman17c.html},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[Feldman17]</span> Provides a characterization of SQ learning in terms of new \\\"statistical dimension;\\\" to be seen in view of the poly-factor equivalence between SQ learning and LDP-constrained/memory-constrained learnin (e.g., [KLNRS11,BDD98]). Includes applications to memory-limited streaming and communication-limited learning.</div>}\\n}\\n  \\n\",\"author_short\":[\"Feldman, V.\"],\"editor_short\":[\"Kale, S.\",\"Shamir, O.\"],\"key\":\"Feldman17\",\"id\":\"Feldman17\",\"bibbaseid\":\"feldman-ageneralcharacterizationofthestatisticalquerycomplexity-2017\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://proceedings.mlr.press/v65/feldman17c.html\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Gill\"],\"firstnames\":[\"Richard\",\"D.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Levit\"],\"firstnames\":[\"Boris\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Applications of the Van Trees inequality: a Bayesian Cramér-Rao bound\",\"journal\":\"Bernoulli\",\"fjournal\":\"Bernoulli. Official Journal of the Bernoulli Society for Mathematical Statistics and Probability\",\"volume\":\"1\",\"year\":\"1995\",\"number\":\"1-2\",\"pages\":\"59–79\",\"issn\":\"1350-7265\",\"mrclass\":\"62F10\",\"mrnumber\":\"1354456\",\"mrreviewer\":\"V. K. Rohatgi\",\"doi\":\"10.2307/3318681\",\"url\":\"https://doi.org/10.2307/3318681\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[GL95]</span> Provides a good and self-contained primer and derivation of the van Trees inequality and its uses.</div>\",\"bibtex\":\"@article{GillR95,\\n    AUTHOR = {Gill, Richard D. and Levit, Boris Y.},\\n     TITLE = {Applications of the {V}an {T}rees inequality: a {B}ayesian\\n              {C}ram\\\\'{e}r-{R}ao bound},\\n   JOURNAL = {Bernoulli},\\n  FJOURNAL = {Bernoulli. Official Journal of the Bernoulli Society for\\n              Mathematical Statistics and Probability},\\n    VOLUME = {1},\\n      YEAR = {1995},\\n    NUMBER = {1-2},\\n     PAGES = {59--79},\\n      ISSN = {1350-7265},\\n   MRCLASS = {62F10},\\n  MRNUMBER = {1354456},\\nMRREVIEWER = {V. K. Rohatgi},\\n       DOI = {10.2307/3318681},\\n       URL = {https://doi.org/10.2307/3318681},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[GL95]</span> Provides a good and self-contained primer and derivation of the van Trees inequality and its uses.</div>} \\n}\\n\\n\",\"author_short\":[\"Gill, R. D.\",\"Levit, B. Y.\"],\"key\":\"GillR95\",\"id\":\"GillR95\",\"bibbaseid\":\"gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.2307/3318681\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Uri\"],\"propositions\":[],\"lastnames\":[\"Meir\"],\"suffixes\":[]},{\"firstnames\":[\"Dor\"],\"propositions\":[],\"lastnames\":[\"Minzer\"],\"suffixes\":[]},{\"firstnames\":[\"Rotem\"],\"propositions\":[],\"lastnames\":[\"Oshman\"],\"suffixes\":[]}],\"title\":\"Can Distributed Uniformity Testing Be Local?\",\"booktitle\":\"2019 ACM Symposium on Principles of Distributed Computing, PODC 2019\",\"pages\":\"228–237\",\"publisher\":\"ACM\",\"year\":\"2019\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[MMO19]</span> Considers a similar setting as [FMO18], but allowing $\\\\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\\\\ell$-bit Boolean function.</div>\",\"bibtex\":\"@inproceedings{MMO19,\\n  author    = {Uri Meir and\\n               Dor Minzer and\\n               Rotem Oshman},\\n  title     = {Can Distributed Uniformity Testing Be Local?},\\n  booktitle = {2019 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2019},\\n  pages     = {228--237},\\n  publisher = {{ACM}},\\n  year      = {2019},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[MMO19]</span> Considers a similar setting as [FMO18], but allowing $\\\\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\\\\ell$-bit Boolean function.</div>}\\n}\\n\\n\",\"author_short\":[\"Meir, U.\",\"Minzer, D.\",\"Oshman, R.\"],\"key\":\"MMO19\",\"id\":\"MMO19\",\"bibbaseid\":\"meir-minzer-oshman-candistributeduniformitytestingbelocal-2019\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Communication and Memory Efficient Testing of Discrete Distributions\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Diakonikolas\"],\"firstnames\":[\"Ilias\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Gouleakis\"],\"firstnames\":[\"Themis\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kane\"],\"firstnames\":[\"Daniel\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rao\"],\"firstnames\":[\"Sankeerth\"],\"suffixes\":[]}],\"booktitle\":\"32nd Conference on Learning Theory, COLT 2019\",\"pages\":\"1070–1106\",\"year\":\"2019\",\"volume\":\"99\",\"series\":\"Proceedings of Machine Learning Research\",\"publisher\":\"PMLR\",\"pdf\":\"http://proceedings.mlr.press/v99/diakonikolas19a/diakonikolas19a.pdf\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DGKR19]</span> Considers global memory constraints, in the blackboard model: the communication bound is for the total communication over all users, and as such the results are incomparable to works on local constraints, though some of the techniques can carry over. Establish tight or near-tight bounds for identity testing of discrete distributions; the techniques also apply to testing under memory constraints.</div>\",\"bibtex\":\"@inproceedings{DGKR19,\\n  title = \\t {Communication and Memory Efficient Testing of Discrete Distributions},\\n  author = \\t {Diakonikolas, Ilias and Gouleakis, Themis and Kane, Daniel M. and Rao, Sankeerth},\\n  booktitle = \\t {32nd Conference on Learning Theory, {COLT} 2019},\\n  pages = \\t {1070--1106},\\n  year = \\t {2019},\\n  volume = \\t {99},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  publisher = \\t {PMLR},\\n  pdf = \\t {http://proceedings.mlr.press/v99/diakonikolas19a/diakonikolas19a.pdf},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DGKR19]</span> Considers global memory constraints, in the blackboard model: the communication bound is for the total communication over all users, and as such the results are incomparable to works on local constraints, though some of the techniques can carry over. Establish tight or near-tight bounds for identity testing of discrete distributions; the techniques also apply to testing under memory constraints.</div>}\\n}\\n\\n\",\"author_short\":[\"Diakonikolas, I.\",\"Gouleakis, T.\",\"Kane, D. M.\",\"Rao, S.\"],\"key\":\"DGKR19\",\"id\":\"DGKR19\",\"bibbaseid\":\"diakonikolas-gouleakis-kane-rao-communicationandmemoryefficienttestingofdiscretedistributions-2019\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Mark\"],\"propositions\":[],\"lastnames\":[\"Braverman\"],\"suffixes\":[]},{\"firstnames\":[\"Ankit\"],\"propositions\":[],\"lastnames\":[\"Garg\"],\"suffixes\":[]},{\"firstnames\":[\"Tengyu\"],\"propositions\":[],\"lastnames\":[\"Ma\"],\"suffixes\":[]},{\"firstnames\":[\"Huy\",\"L.\"],\"propositions\":[],\"lastnames\":[\"Nguyen\"],\"suffixes\":[]},{\"firstnames\":[\"David\",\"P.\"],\"propositions\":[],\"lastnames\":[\"Woodruff\"],\"suffixes\":[]}],\"title\":\"Communication lower bounds for statistical estimation problems via a distributed data processing inequality\",\"booktitle\":\"Symposium on Theory of Computing Conference, STOC'16\",\"pages\":\"1011–1020\",\"publisher\":\"ACM\",\"year\":\"2016\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BGMNW16]</span> Significantly generalizes [GMN14], extending the lower bounds to the blackboard model, and the upper bounds to the SMP model. Includes tight results for sparse mean estimation. The lower bounds are obtained via a combination of strong data processing inequalities (SDPI) and the \\\"cut-and-paste\\\" property of Hellinger distance.</div>\",\"bibtex\":\"@inproceedings{BGMNW16,\\n  author    = {Mark Braverman and\\n               Ankit Garg and\\n               Tengyu Ma and\\n               Huy L. Nguyen and\\n               David P. Woodruff},\\n  title     = {Communication lower bounds for statistical estimation problems via\\n               a distributed data processing inequality},\\n  booktitle = {Symposium on Theory of Computing Conference, {STOC'16}},\\n  pages     = {1011--1020},\\n  publisher = {{ACM}},\\n  year      = {2016},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BGMNW16]</span> Significantly generalizes [GMN14], extending the lower bounds to the blackboard model, and the upper bounds to the SMP model. Includes tight results for sparse mean estimation. The lower bounds are obtained via a combination of strong data processing inequalities (SDPI) and the \\\"cut-and-paste\\\" property of Hellinger distance.</div>}\\n}\\n\\n\",\"author_short\":[\"Braverman, M.\",\"Garg, A.\",\"Ma, T.\",\"Nguyen, H. L.\",\"Woodruff, D. P.\"],\"key\":\"BGMNW16\",\"id\":\"BGMNW16\",\"bibbaseid\":\"braverman-garg-ma-nguyen-woodruff-communicationlowerboundsforstatisticalestimationproblemsviaadistributeddataprocessinginequality-2016\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Decentralized detection\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tsitsiklis\"],\"firstnames\":[\"John\",\"N.\"],\"suffixes\":[]}],\"booktitle\":\"Advances in Statistical Signal Processing\",\"year\":\"1993\",\"volume\":\"2\",\"editor\":[{\"firstnames\":[\"H.\",\"V.\"],\"propositions\":[],\"lastnames\":[\"Poor\"],\"suffixes\":[]},{\"firstnames\":[\"J.\",\"B.\"],\"propositions\":[],\"lastnames\":[\"Thomas\"],\"suffixes\":[]}],\"publisher\":\"JAI Press\",\"pages\":\"297–344\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[Tsi93]</span> Considers <em>simple</em> hypothesis testing in a distributed setting, under communication constraints, and shows that for this problem public-coin (noninteractive) protocols are no more powerful than private-coin protocols.</div>\",\"bibtex\":\"@inproceedings{Tsitsiklis93,\\n  title={Decentralized detection},\\n  author={Tsitsiklis, John N.},\\n  booktitle={Advances in Statistical Signal Processing},\\n  year={1993},\\n  volume = {2},\\n  editor = {H. V. Poor and J. B. Thomas},\\n  publisher = {JAI Press},\\n  pages = {297--344},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[Tsi93]</span> Considers <em>simple</em> hypothesis testing in a distributed setting, under communication constraints, and shows that for this problem public-coin (noninteractive) protocols are no more powerful than private-coin protocols.</div>}\\n}\\n\\n\",\"author_short\":[\"Tsitsiklis, J. N.\"],\"editor_short\":[\"Poor, H. V.\",\"Thomas, J. B.\"],\"key\":\"Tsitsiklis93\",\"id\":\"Tsitsiklis93\",\"bibbaseid\":\"tsitsiklis-decentralizeddetection-1993\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Distributed Signal Detection under Communication Constraints\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Acharya\"],\"firstnames\":[\"Jayadev\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Canonne\"],\"firstnames\":[\"Clément\",\"L.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"firstnames\":[\"Himanshu\"],\"suffixes\":[]}],\"pages\":\"41–63\",\"year\":\"2020\",\"volume\":\"125\",\"series\":\"Proceedings of Machine Learning Research\",\"publisher\":\"PMLR\",\"pdf\":\"http://proceedings.mlr.press/v125/acharya20b/acharya20b.pdf\",\"url\":\"http://proceedings.mlr.press/v125/acharya20b.html\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20c]</span> Applies the $χ^2$-contraction lower bound framework of [ACT20a] to obtain lower bounds for the problem of Gaussian mean testing (the hypothesis testing version of mean estimation in the Gaussian Location Model) under communication constraints (noninteractive). Also provides upper bounds for both private- and public-coin protocols.</div>\",\"bibtex\":\"@InProceedings{ACT20,\\n  title = \\t {Distributed Signal Detection under Communication Constraints},\\n  author =       {Acharya, Jayadev and Canonne, Cl{\\\\'e}ment L. and Tyagi, Himanshu},\\n  pages = \\t {41--63},\\n  year = \\t {2020},\\n  volume = \\t {125},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  publisher =    {PMLR},\\n  pdf = \\t {http://proceedings.mlr.press/v125/acharya20b/acharya20b.pdf},\\n  url = \\t {http://proceedings.mlr.press/v125/acharya20b.html},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20c]</span> Applies the $χ^2$-contraction lower bound framework of [ACT20a] to obtain lower bounds for the problem of Gaussian mean testing (the hypothesis testing version of mean estimation in the Gaussian Location Model) under communication constraints (noninteractive). Also provides upper bounds for both private- and public-coin protocols.</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L.\",\"Tyagi, H.\"],\"key\":\"ACT20\",\"id\":\"ACT20\",\"bibbaseid\":\"acharya-canonne-tyagi-distributedsignaldetectionundercommunicationconstraints-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://proceedings.mlr.press/v125/acharya20b.html\"},\"metadata\":{\"authorlinks\":{\"canonne, c\":\"https://ccanonne.github.io/\"}},\"downloads\":21,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Yanjun\"],\"propositions\":[],\"lastnames\":[\"Han\"],\"suffixes\":[]},{\"firstnames\":[\"Pritam\"],\"propositions\":[],\"lastnames\":[\"Mukherjee\"],\"suffixes\":[]},{\"firstnames\":[\"Ayfer\"],\"propositions\":[],\"lastnames\":[\"Özgür\"],\"suffixes\":[]},{\"firstnames\":[\"Tsachy\"],\"propositions\":[],\"lastnames\":[\"Weissman\"],\"suffixes\":[]}],\"title\":\"Distributed Statistical Estimation of High-Dimensional and Non-parametric Distributions\",\"booktitle\":\"2018 IEEE International Symposium on Information Theory (ISIT'18)\",\"year\":\"2018\",\"pages\":\"506–510\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[HMÖW18]</span> Lower bounds on distributed estimation (in total variation distance) of several families of distributions under communication constraints. Results apply to noniteractive protocols (a gap in the argument prevents the extension to interactive).</div>\",\"bibtex\":\"@inproceedings{HMOW-ISIT18,\\n  author    = {Yanjun Han and Pritam Mukherjee and Ayfer {{\\\\\\\"O}zg{\\\\\\\"u}r} and Tsachy Weissman},\\n  title = {Distributed Statistical Estimation of High-Dimensional and Non-parametric Distributions},\\n  booktitle = {2018 IEEE International Symposium on Information Theory (ISIT'18)},\\nyear = {2018},\\npages={506--510},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[HMÖW18]</span> Lower bounds on distributed estimation (in total variation distance) of several families of distributions under communication constraints. Results apply to noniteractive protocols (a gap in the argument prevents the extension to interactive).</div>}\\n}\\n\\n\",\"author_short\":[\"Han, Y.\",\"Mukherjee, P.\",\"Özgür, A.\",\"Weissman, T.\"],\"key\":\"HMOW-ISIT18\",\"id\":\"HMOW-ISIT18\",\"bibbaseid\":\"han-mukherjee-zgr-weissman-distributedstatisticalestimationofhighdimensionalandnonparametricdistributions-2018\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Orr\"],\"propositions\":[],\"lastnames\":[\"Fischer\"],\"suffixes\":[]},{\"firstnames\":[\"Uri\"],\"propositions\":[],\"lastnames\":[\"Meir\"],\"suffixes\":[]},{\"firstnames\":[\"Rotem\"],\"propositions\":[],\"lastnames\":[\"Oshman\"],\"suffixes\":[]}],\"title\":\"Distributed Uniformity Testing\",\"booktitle\":\"2018 ACM Symposium on Principles of Distributed Computing, PODC 2018\",\"pages\":\"455–464\",\"publisher\":\"ACM\",\"year\":\"2018\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[FMO18]</span> Studies distributed uniformity testing in a setting where each user observe multiple samples, and communicates a single bit to the referee who is required to use a simple aggregation rule, e.g., AND or a threshold. The goal is then to minimize the number of samples required per user. Also contains results on uniformity testing in other distributed models, such as the CONGEST or LOCAL models.</div>\",\"bibtex\":\"@inproceedings{FMO18,\\n  author    = {Orr Fischer and\\n               Uri Meir and\\n               Rotem Oshman},\\n  title     = {Distributed Uniformity Testing},\\n  booktitle = {2018 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2018},\\n  pages     = {455--464},\\n  publisher = {{ACM}},\\n  year      = {2018},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[FMO18]</span> Studies distributed uniformity testing in a setting where each user observe  multiple samples, and  communicates a single bit to the referee who  is  required  to  use a simple  aggregation rule, e.g., AND or a threshold. The goal is then to minimize the number of samples required per user. Also contains results on uniformity testing in other distributed models, such as the CONGEST or LOCAL models.</div>}\\n}\\n\\n\",\"author_short\":[\"Fischer, O.\",\"Meir, U.\",\"Oshman, R.\"],\"key\":\"FMO18\",\"id\":\"FMO18\",\"bibbaseid\":\"fischer-meir-oshman-distributeduniformitytesting-2018\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit\",\"author\":[{\"firstnames\":[\"Jayadev\"],\"propositions\":[],\"lastnames\":[\"Acharya\"],\"suffixes\":[]},{\"firstnames\":[\"Clément\",\"L\"],\"propositions\":[],\"lastnames\":[\"Canonne\"],\"suffixes\":[]},{\"firstnames\":[\"Yanjun\"],\"propositions\":[],\"lastnames\":[\"Han\"],\"suffixes\":[]},{\"firstnames\":[\"Ziteng\"],\"propositions\":[],\"lastnames\":[\"Sun\"],\"suffixes\":[]},{\"firstnames\":[\"Himanshu\"],\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"suffixes\":[]}],\"booktitle\":\"33rd Conference on Learning Theory, COLT 2020\",\"pages\":\"3–40\",\"year\":\"2020\",\"volume\":\"125\",\"series\":\"Proceedings of Machine Learning Research\",\"publisher\":\"PMLR\",\"pdf\":\"http://proceedings.mlr.press/v125/acharya20a/acharya20a.pdf\",\"url\":\"http://proceedings.mlr.press/v125/acharya20a.html\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACHST20]</span> Similar noninteractive setting as [ACT20a,ACT20b,ACFST20], for general local information constraints. Focus on the tight tradeoff between amount of public randomness available and sample complexity, for identity testing (goodness-of-fit).</div>\",\"bibtex\":\"@inproceedings{ACHST20,\\n  title = \\t {Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit},\\n  author = \\t {Jayadev Acharya and Clément L Canonne and Yanjun Han and Ziteng Sun and Himanshu Tyagi},\\n  booktitle = \\t {33rd Conference on Learning Theory, {COLT} 2020},\\n  pages = \\t {3--40},\\n  year = \\t {2020},\\n  volume = \\t {125},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  publisher = \\t {PMLR},\\n  pdf = \\t {http://proceedings.mlr.press/v125/acharya20a/acharya20a.pdf},\\n  url = \\t {http://proceedings.mlr.press/v125/acharya20a.html},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACHST20]</span> Similar noninteractive setting as [ACT20a,ACT20b,ACFST20], for general local information constraints. Focus on the tight tradeoff between amount of public randomness available and sample complexity, for identity testing (goodness-of-fit).</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L\",\"Han, Y.\",\"Sun, Z.\",\"Tyagi, H.\"],\"key\":\"ACHST20\",\"id\":\"ACHST20\",\"bibbaseid\":\"acharya-canonne-han-sun-tyagi-domaincompressionanditsapplicationtorandomnessoptimaldistributedgoodnessoffit-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://proceedings.mlr.press/v125/acharya20a.html\"},\"metadata\":{\"authorlinks\":{\"canonne, c\":\"https://ccanonne.github.io/\"}},\"downloads\":62,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Sébastien\"],\"propositions\":[],\"lastnames\":[\"Bubeck\"],\"suffixes\":[]},{\"firstnames\":[\"Sitan\"],\"propositions\":[],\"lastnames\":[\"Chen\"],\"suffixes\":[]},{\"firstnames\":[\"Jerry\"],\"propositions\":[],\"lastnames\":[\"Li\"],\"suffixes\":[]}],\"title\":\"Entanglement is Necessary for Optimal Quantum Property Testing\",\"journal\":\"CoRR\",\"volume\":\"abs/2004.07869\",\"year\":\"2020\",\"note\":\"To appear in FOCS'20.\",\"url\":\"https://arxiv.org/abs/2004.07869\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BCL20]</span> Consider the task of testing whether a quantum state is maximally mixed vs. far from it in trace distance, given \\\"local measurements\\\" (no entanglement). Establishes a separation between non-adaptive (noninteractive) and adaptive (sequentially interactive) algorithms for this task. Even though this question does not, per se, fall under the same setting as distributed uniformity testing and the works are independent, the ideas bear resemblance to the $χ^2$-contraction lower bound framework of [ACT20a].</div>\",\"bibtex\":\"@article{BCL20,\\n  author    = {S{\\\\'{e}}bastien Bubeck and\\n               Sitan Chen and\\n               Jerry Li},\\n  title     = {Entanglement is Necessary for Optimal Quantum Property Testing},\\n  journal   = {CoRR},\\n  volume    = {abs/2004.07869},\\n  year      = {2020},\\n  note   = {To appear in FOCS'20.},\\n  url = {https://arxiv.org/abs/2004.07869},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BCL20]</span> Consider the task of testing whether a quantum state is maximally mixed vs. far from it in trace distance, given \\\"local measurements\\\" (no entanglement). Establishes a separation between non-adaptive (noninteractive) and adaptive (sequentially interactive) algorithms for this task. Even though this question does not, per se, fall under the same setting as distributed uniformity testing and the works are independent, the ideas bear resemblance to the $χ^2$-contraction lower bound framework of [ACT20a].</div>}\\n}\\n\\n\",\"author_short\":[\"Bubeck, S.\",\"Chen, S.\",\"Li, J.\"],\"key\":\"BCL20\",\"id\":\"BCL20\",\"bibbaseid\":\"bubeck-chen-li-entanglementisnecessaryforoptimalquantumpropertytesting-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/2004.07869\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Leighton\",\"P.\"],\"propositions\":[],\"lastnames\":[\"Barnes\"],\"suffixes\":[]},{\"firstnames\":[\"Yanjun\"],\"propositions\":[],\"lastnames\":[\"Han\"],\"suffixes\":[]},{\"firstnames\":[\"Ayfer\"],\"propositions\":[],\"lastnames\":[\"Özgür\"],\"suffixes\":[]}],\"title\":\"Fisher Information for Distributed Estimation under a Blackboard Communication Protocol\",\"booktitle\":\"ISIT\",\"pages\":\"2704–2708\",\"publisher\":\"IEEE\",\"year\":\"2019\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BHÖ19]</span> Provides general lower bounds for parameter estimation (and, in some cases, nonparametric density estimation) under $\\\\ell_2$ loss for interactive protocols (blackboard model) under communication constraints, and instantiate it to obtain tight bounds for various statistical models such as Gaussian, product Bernoulli, and discrete distribution estimation. At its core, the lower bounds rely on a Cramér–Rao/van Trees-type approach, which leaves the (trace of) the Fisher information matrix as quantity to analyze to get lower bounds.</div>\",\"bibtex\":\"@inproceedings{BHO19,\\n  author    = {Leighton P. Barnes and\\n               Yanjun Han and\\n               Ayfer {\\\\\\\"{O}}zg{\\\\\\\"{u}}r},\\n  title     = {Fisher Information for Distributed Estimation under a Blackboard Communication Protocol},\\n  booktitle = {{ISIT}},\\n  pages     = {2704--2708},\\n  publisher = {{IEEE}},\\n  year      = {2019},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BHÖ19]</span> Provides general lower bounds for parameter estimation (and, in some cases, nonparametric density estimation) under $\\\\ell_2$ loss for interactive protocols (blackboard model) under communication constraints, and instantiate it to obtain tight bounds for various statistical models such as Gaussian, product Bernoulli, and discrete distribution estimation. At its core, the lower bounds rely on a Cramér–Rao/van Trees-type approach, which leaves the (trace of) the Fisher information matrix as quantity to analyze to get lower bounds.</div>}\\n}\\n\\n\",\"author_short\":[\"Barnes, L. P.\",\"Han, Y.\",\"Özgür, A.\"],\"key\":\"BHO19\",\"id\":\"BHO19\",\"bibbaseid\":\"barnes-han-zgr-fisherinformationfordistributedestimationunderablackboardcommunicationprotocol-2019\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Leighton\",\"P.\"],\"propositions\":[],\"lastnames\":[\"Barnes\"],\"suffixes\":[]},{\"firstnames\":[\"Wei-Ning\"],\"propositions\":[],\"lastnames\":[\"Chen\"],\"suffixes\":[]},{\"firstnames\":[\"Ayfer\"],\"propositions\":[],\"lastnames\":[\"Özgür\"],\"suffixes\":[]}],\"title\":\"Fisher information under local differential privacy\",\"journal\":\"CoRR\",\"volume\":\"abs/2005.10783\",\"url\":\"https://arxiv.org/abs/2005.10783\",\"year\":\"2020\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BCÖ20]</span> Provides lower bounds for parameter estimation under $\\\\ell_2$ loss for interactive protocols (blackboard model) under local privacy, and instantiate it to obtain tight bounds for Gaussian mean estimation, (sparse) Bernoulli mean estimation, and discrete distribution estimation. As in [BHÖ19], the lower bound framework is based on a Cramér–Rao/van Trees-type approach.\",\"note\":\"Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT).</div>\",\"bibtex\":\"@article{BCO20,\\n  author    = {Leighton P. Barnes and\\n               Wei{-}Ning Chen and\\n               Ayfer {\\\\\\\"{O}}zg{\\\\\\\"{u}}r},\\n  title     = {Fisher information under local differential privacy},\\n  journal   = {CoRR},\\n  volume    = {abs/2005.10783},\\n  url = {https://arxiv.org/abs/2005.10783},\\n  year      = {2020},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BCÖ20]</span> Provides lower bounds for parameter estimation under $\\\\ell_2$ loss for interactive protocols (blackboard model) under local privacy, and instantiate it to obtain tight bounds for Gaussian mean estimation, (sparse) Bernoulli mean estimation, and discrete distribution estimation. As in [BHÖ19], the lower bound framework is based on a Cramér–Rao/van Trees-type approach.},\\n  note = {Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT).</div>}\\n}\\n\\n\",\"author_short\":[\"Barnes, L. P.\",\"Chen, W.\",\"Özgür, A.\"],\"key\":\"BCO20\",\"id\":\"BCO20\",\"bibbaseid\":\"barnes-chen-zgr-fisherinformationunderlocaldifferentialprivacy-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/2005.10783\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Fundamental limits of online and distributed algorithms for statistical learning and estimation\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Shamir\"],\"firstnames\":[\"Ohad\"],\"suffixes\":[]}],\"booktitle\":\"Advances in Neural Information Processing Systems 27, NeurIPS'14\",\"pages\":\"163–171\",\"year\":\"2014\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[Sha14]</span> Considers estimation tasks under various information constraints, such as memory or communication. Establishes results for sequentially interactive protocols for those problems by proving a lower bound on the \\\"hide-and-seek\\\" problem, that is, the mean estimation problem for high-dimensional product Bernoulli distributions with 1-sparse mean vectors.</div>\",\"bibtex\":\"@inproceedings{Shamir14,\\n  title={Fundamental limits of online and distributed algorithms for statistical learning and estimation},\\n  author={Shamir, Ohad},\\n  booktitle= {Advances in Neural Information Processing Systems 27, {NeurIPS'14}},\\n  pages={163--171},\\n  year={2014},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[Sha14]</span> Considers estimation tasks under various information constraints, such as memory or communication. Establishes results for sequentially interactive protocols for those problems by proving a lower bound on the \\\"hide-and-seek\\\" problem, that is, the mean estimation problem for high-dimensional product Bernoulli distributions with 1-sparse mean vectors.</div>}\\n}\\n\\n\",\"author_short\":[\"Shamir, O.\"],\"key\":\"Shamir14\",\"id\":\"Shamir14\",\"bibbaseid\":\"shamir-fundamentallimitsofonlineanddistributedalgorithmsforstatisticallearningandestimation-2014\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Jayadev\"],\"propositions\":[],\"lastnames\":[\"Acharya\"],\"suffixes\":[]},{\"firstnames\":[\"Clément\",\"L.\"],\"propositions\":[],\"lastnames\":[\"Canonne\"],\"suffixes\":[]},{\"firstnames\":[\"Himanshu\"],\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"suffixes\":[]}],\"title\":\"General lower bounds for interactive high-dimensional estimation under information constraints\",\"journal\":\"CoRR\",\"volume\":\"abs/2010.06562\",\"year\":\"2020\",\"url\":\"https://arxiv.org/abs/2010.06562\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20d]</span> Abstracts and generalizes the lower bound framework of [ACLST20] to provide \\\"plug-and-play\\\" lower bounds for parameter estimation with sequentially interactive protocolunder general information constraints. Instantiates them to get lower bounds for $\\\\ell_p$ losses in the cases of discrete distribution estimation, Gaussian mean estimation, and product Bernoulli mean estimation; and complements them with upper bounds.</div>\",\"bibtex\":\"@article{ACT20:HD,\\n  author    = {Jayadev Acharya and\\n               Cl{\\\\'{e}}ment L. Canonne and\\n               Himanshu Tyagi},\\n  title     = {General lower bounds for interactive high-dimensional estimation under\\n               information constraints},\\n  journal   = {CoRR},\\n  volume    = {abs/2010.06562},\\n  year      = {2020},\\n  url = {https://arxiv.org/abs/2010.06562},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20d]</span> Abstracts and generalizes the lower bound framework of [ACLST20] to provide \\\"plug-and-play\\\" lower bounds for parameter estimation with sequentially interactive protocolunder general information constraints. Instantiates them to get lower bounds for $\\\\ell_p$ losses in the cases of discrete distribution estimation, Gaussian mean estimation, and product Bernoulli mean estimation; and complements them with upper bounds.</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L.\",\"Tyagi, H.\"],\"key\":\"ACT20:HD\",\"id\":\"ACT20:HD\",\"bibbaseid\":\"acharya-canonne-tyagi-generallowerboundsforinteractivehighdimensionalestimationunderinformationconstraints-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/2010.06562\"},\"metadata\":{\"authorlinks\":{\"canonne, c\":\"https://ccanonne.github.io/\"}},\"downloads\":65,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Yanjun\"],\"propositions\":[],\"lastnames\":[\"Han\"],\"suffixes\":[]},{\"firstnames\":[\"Ayfer\"],\"propositions\":[],\"lastnames\":[\"Özgür\"],\"suffixes\":[]},{\"firstnames\":[\"Tsachy\"],\"propositions\":[],\"lastnames\":[\"Weissman\"],\"suffixes\":[]}],\"title\":\"Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints\",\"booktitle\":\"31st Conference on Learning Theory, COLT 2018\",\"series\":\"Proceedings of Machine Learning Research\",\"volume\":\"75\",\"pages\":\"3163–3188\",\"publisher\":\"PMLR\",\"year\":\"2018\",\"note\":\"See updated version, ˘rlhttps://arxiv.org/abs/1802.08417v3 (2020).\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[HÖW18]</span> Lower bounds on distributed parameter estimation under the $\\\\ell_2$ loss of several families of distributions, including high-dimensional, under communication constraints. Results for the latest version, using techniques similar to those of [ACLST20,ACT20d], extend to the blackboard model and include $\\\\ell_p$ losses.</div>\",\"bibtex\":\"@inproceedings{HOW18,\\n  author    = {Yanjun Han and\\n               Ayfer {\\\\\\\"{O}}zg{\\\\\\\"{u}}r and\\n               Tsachy Weissman},\\n  title     = {Geometric Lower Bounds for Distributed Parameter Estimation under\\n               Communication Constraints},\\n  booktitle = {31st Conference on Learning Theory, {COLT} 2018},\\n  series    = {Proceedings of Machine Learning Research},\\n  volume    = {75},\\n  pages     = {3163--3188},\\n  publisher = {{PMLR}},\\n  year      = {2018},\\n  note = {See updated version, \\\\url{https://arxiv.org/abs/1802.08417v3} (2020).},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[HÖW18]</span> Lower bounds on distributed parameter estimation under the $\\\\ell_2$ loss of several families of distributions, including high-dimensional, under communication constraints. Results for the latest version, using techniques similar to those of [ACLST20,ACT20d], extend to the blackboard model and include $\\\\ell_p$ losses.</div>}\\n}\\n\\n\",\"author_short\":[\"Han, Y.\",\"Özgür, A.\",\"Weissman, T.\"],\"key\":\"HOW18\",\"id\":\"HOW18\",\"bibbaseid\":\"han-zgr-weissman-geometriclowerboundsfordistributedparameterestimationundercommunicationconstraints-2018\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Acharya\"],\"firstnames\":[\"Jayadev\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Canonne\"],\"firstnames\":[\"Clément\",\"L.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"firstnames\":[\"Himanshu\"],\"suffixes\":[]}],\"journal\":\"IEEE Transactions on Information Theory\",\"year\":\"2020\",\"note\":\"Conference version in COLT'19\",\"url\":\"https://arxiv.org/abs/1812.11476\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20a]</span> Provides a unified lower bound framework to derive sample complexity lower bounds for noninteractive protocols under general local information constraints, captured by a characterization of $\\\\mathcal{W}$ in terms of various norms of a p.s.d. matrix $H(W)$.</div>\",\"bibtex\":\"@article{ACT19:LB,\\n  title = \\t {Inference under Information Constraints {I}: Lower Bounds from Chi-Square Contraction},\\n  author = \\t {Acharya, Jayadev and Canonne, Cl{\\\\'{e}}ment L. and Tyagi, Himanshu},\\n  journal = \\t {IEEE Transactions on Information Theory},\\n  year = \\t {2020},\\n  note = {Conference version in {COLT'19}},\\n  url = {https://arxiv.org/abs/1812.11476},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20a]</span> Provides a unified lower bound framework to derive sample complexity lower bounds for noninteractive protocols under general local information constraints, captured by a characterization of $\\\\mathcal{W}$ in terms of various norms of a p.s.d. matrix $H(W)$.</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L.\",\"Tyagi, H.\"],\"key\":\"ACT19:LB\",\"id\":\"ACT19:LB\",\"bibbaseid\":\"acharya-canonne-tyagi-inferenceunderinformationconstraintsilowerboundsfromchisquarecontraction-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/1812.11476\"},\"metadata\":{\"authorlinks\":{\"canonne, c\":\"https://ccanonne.github.io/\"}},\"downloads\":70,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Inference under Information Constraints II: Communication Constraints and Shared Randomness\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Acharya\"],\"firstnames\":[\"Jayadev\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Canonne\"],\"firstnames\":[\"Clément\",\"L.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"firstnames\":[\"Himanshu\"],\"suffixes\":[]}],\"journal\":\"IEEE Transactions on Information Theory\",\"year\":\"2020\",\"note\":\"Conference version in ICML'19\",\"url\":\"https://arxiv.org/abs/1905.08302\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20b]</span> Focuses on the communication constraints ($\\\\ell$ bits per player), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a].</div>\",\"bibtex\":\"@article{ACT19:UB,\\n  title = \\t {Inference under Information Constraints {II}: Communication Constraints and Shared Randomness},\\n  author = \\t {Acharya, Jayadev and Canonne, Cl{\\\\'{e}}ment L. and Tyagi, Himanshu},\\n  journal = {IEEE Transactions on Information Theory},\\n  year = \\t {2020},\\n  note = {Conference version in {ICML'19}},\\n  url = {https://arxiv.org/abs/1905.08302},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACT20b]</span> Focuses on the communication constraints ($\\\\ell$ bits per player), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a].</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L.\",\"Tyagi, H.\"],\"key\":\"ACT19:UB\",\"id\":\"ACT19:UB\",\"bibbaseid\":\"acharya-canonne-tyagi-inferenceunderinformationconstraintsiicommunicationconstraintsandsharedrandomness-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/1905.08302\"},\"metadata\":{\"authorlinks\":{\"canonne, c\":\"https://ccanonne.github.io/\"}},\"downloads\":44,\"html\":\"\"},{\"bibtype\":\"misc\",\"type\":\"misc\",\"author\":[{\"firstnames\":[\"Jayadev\"],\"propositions\":[],\"lastnames\":[\"Acharya\"],\"suffixes\":[]},{\"firstnames\":[\"Clément\",\"L.\"],\"propositions\":[],\"lastnames\":[\"Canonne\"],\"suffixes\":[]},{\"firstnames\":[\"Cody\"],\"propositions\":[],\"lastnames\":[\"Freitag\"],\"suffixes\":[]},{\"firstnames\":[\"Ziteng\"],\"propositions\":[],\"lastnames\":[\"Sun\"],\"suffixes\":[]},{\"firstnames\":[\"Himanshu\"],\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"suffixes\":[]}],\"title\":\"Inference under Information Constraints III: Local Privacy Constraints\",\"note\":\"Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT). Preprint available at arXiv:abs/1808.02174; Conference version in AISTATS'19\",\"year\":\"2020\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACFST20]</span> Focuses on the local privacy constraints (ρ-LDP), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a]. Also contains lower bounds for independence testing under LDP.</div>\",\"bibtex\":\"@misc{ACFST19,\\n  author    = {Jayadev Acharya and\\n               Cl{\\\\'{e}}ment L. Canonne and\\n              Cody Freitag and Ziteng Sun\\n              and Himanshu Tyagi},\\n  title     = {Inference under Information Constraints {III}: Local Privacy Constraints},\\n  note = {Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT). Preprint available at arXiv:abs/1808.02174; Conference version in {AISTATS'19}},\\n  year      = {2020},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACFST20]</span> Focuses on the local privacy constraints (ρ-LDP), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a]. Also contains lower bounds for independence testing under LDP.</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L.\",\"Freitag, C.\",\"Sun, Z.\",\"Tyagi, H.\"],\"key\":\"ACFST19\",\"id\":\"ACFST19\",\"bibbaseid\":\"acharya-canonne-freitag-sun-tyagi-inferenceunderinformationconstraintsiiilocalprivacyconstraints-2020\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Information-theoretic lower bounds for distributed statistical estimation with communication constraints\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhang\"],\"firstnames\":[\"Yuchen\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Duchi\"],\"firstnames\":[\"John\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Jordan\"],\"firstnames\":[\"Michael\",\"I.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wainwright\"],\"firstnames\":[\"Martin\",\"J.\"],\"suffixes\":[]}],\"booktitle\":\"Advances in Neural Information Processing Systems 26, NeurIPS'13\",\"pages\":\"2328–2336\",\"year\":\"2013\",\"url\":\"https://arxiv.org/abs/1405.0782\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ZDJW13]</span> and <span class=\\\"bluecite\\\">[DJWZ14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols under communication constraints under $\\\\ell_2$ loss for various estimation problems, including Gaussian and Bernoulli mean estimation. Also includes some results for interactive protocols.</div>\",\"bibtex\":\"@inproceedings{ZDJW13,\\n  title={Information-theoretic lower bounds for distributed statistical estimation with communication constraints},\\n  author={Zhang, Yuchen and Duchi, John and Jordan, Michael I. and Wainwright, Martin J.},\\n  booktitle= {Advances in Neural Information Processing Systems 26, {NeurIPS'13}},\\n  pages={2328--2336},\\n  year={2013},\\n  url = {https://arxiv.org/abs/1405.0782},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ZDJW13]</span> and <span class=\\\"bluecite\\\">[DJWZ14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols  under communication constraints under $\\\\ell_2$ loss for various estimation problems, including Gaussian and Bernoulli mean estimation. Also includes some results for interactive protocols.</div>}\\n}\\n\\n\",\"author_short\":[\"Zhang, Y.\",\"Duchi, J.\",\"Jordan, M. I.\",\"Wainwright, M. J.\"],\"key\":\"ZDJW13\",\"id\":\"ZDJW13\",\"bibbaseid\":\"zhang-duchi-jordan-wainwright-informationtheoreticlowerboundsfordistributedstatisticalestimationwithcommunicationconstraints-2013\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/1405.0782\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Jayadev\"],\"propositions\":[],\"lastnames\":[\"Acharya\"],\"suffixes\":[]},{\"firstnames\":[\"Clément\",\"L.\"],\"propositions\":[],\"lastnames\":[\"Canonne\"],\"suffixes\":[]},{\"firstnames\":[\"Yuhan\"],\"propositions\":[],\"lastnames\":[\"Liu\"],\"suffixes\":[]},{\"firstnames\":[\"Ziteng\"],\"propositions\":[],\"lastnames\":[\"Sun\"],\"suffixes\":[]},{\"firstnames\":[\"Himanshu\"],\"propositions\":[],\"lastnames\":[\"Tyagi\"],\"suffixes\":[]}],\"title\":\"Interactive Inference under Information Constraints\",\"journal\":\"CoRR\",\"volume\":\"abs/2007.10976\",\"year\":\"2020\",\"url\":\"https://arxiv.org/abs/2007.10976\",\"archiveprefix\":\"arXiv\",\"eprint\":\"2007.10976\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACLST20]</span> Focuses on density estimation (learning) and goodness-of-fit (identity testing) of discrete distributions with regard to total variation ($\\\\ell_1$ metric), for sequentially interactive protocols under general local information constraints. Implies tight bounds for those problems under LDP and communication constraints.</div>\",\"bibtex\":\"@article{ACLST20,\\n  author    = {Jayadev Acharya and\\n               Cl{\\\\'{e}}ment L. Canonne and\\n               Yuhan Liu and\\n               Ziteng Sun and\\n               Himanshu Tyagi},\\n  title     = {Interactive Inference under Information Constraints},\\n  journal   = {CoRR},\\n  volume    = {abs/2007.10976},\\n  year      = {2020},\\n  url       = {https://arxiv.org/abs/2007.10976},\\n  archivePrefix = {arXiv},\\n  eprint    = {2007.10976},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[ACLST20]</span> Focuses on density estimation (learning) and goodness-of-fit (identity testing) of discrete distributions with regard to total variation ($\\\\ell_1$ metric), for sequentially interactive protocols under general local information constraints. Implies tight bounds for those problems under LDP and communication constraints.</div>}\\n}\\n\\n\",\"author_short\":[\"Acharya, J.\",\"Canonne, C. L.\",\"Liu, Y.\",\"Sun, Z.\",\"Tyagi, H.\"],\"key\":\"ACLST20\",\"id\":\"ACLST20\",\"bibbaseid\":\"acharya-canonne-liu-sun-tyagi-interactiveinferenceunderinformationconstraints-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://arxiv.org/abs/2007.10976\"},\"metadata\":{\"authorlinks\":{\"canonne, c\":\"https://ccanonne.github.io/\"}},\"downloads\":23,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Ben-David\"],\"firstnames\":[\"Shai\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Dichterman\"],\"firstnames\":[\"Eli\"],\"suffixes\":[]}],\"title\":\"Learning with restricted focus of attention\",\"journal\":\"J. Comput. System Sci.\",\"fjournal\":\"Journal of Computer and System Sciences\",\"volume\":\"56\",\"year\":\"1998\",\"number\":\"3\",\"pages\":\"277–298\",\"issn\":\"0022-0000\",\"mrclass\":\"68Q32 (68T05)\",\"mrnumber\":\"1633977\",\"doi\":\"10.1006/jcss.1998.1569\",\"url\":\"https://doi.org/10.1006/jcss.1998.1569\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BDD98]</span> Provides the first connection (and poly-factor equivalence) between learning with communication constraints (wRFA: \\\"restricted focus of attention'') and statistical query (SQ) learning.</div>\",\"bibtex\":\"@article{BenDavidD98,\\n    AUTHOR = {Ben-David, Shai and Dichterman, Eli},\\n     TITLE = {Learning with restricted focus of attention},\\n   JOURNAL = {J. Comput. System Sci.},\\n  FJOURNAL = {Journal of Computer and System Sciences},\\n    VOLUME = {56},\\n      YEAR = {1998},\\n    NUMBER = {3},\\n     PAGES = {277--298},\\n      ISSN = {0022-0000},\\n   MRCLASS = {68Q32 (68T05)},\\n  MRNUMBER = {1633977},\\n       DOI = {10.1006/jcss.1998.1569},\\n       URL = {https://doi.org/10.1006/jcss.1998.1569},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BDD98]</span> Provides the first connection (and poly-factor equivalence) between learning with communication constraints (wRFA: \\\"restricted focus of attention'') and statistical query (SQ) learning.</div>}\\n}\\n\\n\",\"author_short\":[\"Ben-David, S.\",\"Dichterman, E.\"],\"key\":\"BenDavidD98\",\"id\":\"BenDavidD98\",\"bibbaseid\":\"bendavid-dichterman-learningwithrestrictedfocusofattention-1998\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1006/jcss.1998.1569\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"John\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Duchi\"],\"suffixes\":[]},{\"firstnames\":[\"Michael\",\"I.\"],\"propositions\":[],\"lastnames\":[\"Jordan\"],\"suffixes\":[]},{\"firstnames\":[\"Martin\",\"J.\"],\"propositions\":[],\"lastnames\":[\"Wainwright\"],\"suffixes\":[]}],\"title\":\"Local Privacy and Statistical Minimax Rates\",\"booktitle\":\"focs13\",\"pages\":\"429–438\",\"publisher\":\"IEEE Computer Society\",\"year\":\"2013\",\"note\":\"Full version at ˘rlhttps://arxiv.org/abs/1302.3203.\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DJW13]</span> Lower bounds on parameter estimation for several families of distributions under LDP constraints, via strong data processing inequalities (SDPI) and a locally private version of Le Cam, Fano, and Assouad's lemmata. Results apply to the one-dimensional setting, and in high dimensions for noninteractive protocols.</div>\",\"bibtex\":\"@inproceedings{DJW13:FOCS,\\n  author    = {John C. Duchi and\\n               Michael I. Jordan and\\n               Martin J. Wainwright},\\n  title     = {Local Privacy and Statistical Minimax Rates},\\n  booktitle = focs13,\\n  pages     = {429--438},\\n  publisher = {{IEEE} Computer Society},\\n  year      = {2013},\\n  note = {Full version at \\\\url{https://arxiv.org/abs/1302.3203}.},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DJW13]</span> Lower bounds on parameter estimation for several families of distributions under LDP constraints, via strong data processing inequalities (SDPI) and a locally private version of Le Cam, Fano, and Assouad's lemmata. Results apply to the one-dimensional setting, and in high dimensions for noninteractive protocols.</div>}\\n}\\n\\n\",\"author_short\":[\"Duchi, J. C.\",\"Jordan, M. I.\",\"Wainwright, M. J.\"],\"key\":\"DJW13:FOCS\",\"id\":\"DJW13:FOCS\",\"bibbaseid\":\"duchi-jordan-wainwright-localprivacyandstatisticalminimaxrates-2013\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms\",\"author\":[{\"firstnames\":[\"Thomas\",\"B.\"],\"propositions\":[],\"lastnames\":[\"Berrett\"],\"suffixes\":[]},{\"firstnames\":[\"Cristina\"],\"propositions\":[],\"lastnames\":[\"Butucea\"],\"suffixes\":[]}],\"journal\":\"CoRR\",\"year\":\"2020\",\"volume\":\"abs/2005.12601\",\"note\":\"To appear in NeurIPS'20.\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BB20]</span> Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\\\\mathbf{q}$ (while the other two works focus on the worst-case $\\\\mathbf{q}$, i.e., the uniform distribution).</div>\",\"bibtex\":\"@article{BB20,\\n    title={Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms},\\n    author={Thomas B. Berrett and Cristina Butucea},\\n    journal = {CoRR},\\n    year={2020},\\n    volume    = {abs/2005.12601},\\n    note = {To appear in {NeurIPS'20}.},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[BB20]</span> Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\\\\mathbf{q}$ (while the other two works focus on the worst-case $\\\\mathbf{q}$, i.e., the uniform distribution).</div>}\\n}\\n\\n\",\"author_short\":[\"Berrett, T. B.\",\"Butucea, C.\"],\"key\":\"BB20\",\"id\":\"BB20\",\"bibbaseid\":\"berrett-butucea-locallyprivatenonasymptotictestingofdiscretedistributionsisfasterusinginteractivemechanisms-2020\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Lower Bounds for Locally Private Estimation via Communication Complexity\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Duchi\"],\"firstnames\":[\"John\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rogers\"],\"firstnames\":[\"Ryan\"],\"suffixes\":[]}],\"booktitle\":\"32nd Conference on Learning Theory, COLT 2019\",\"pages\":\"1161–1191\",\"year\":\"2019\",\"volume\":\"99\",\"series\":\"Proceedings of Machine Learning Research\",\"publisher\":\"PMLR\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DR19]</span> Develops a communication-complexity-based methodology for lower bounds under LDP constraints in the blackboard communication model. Obtains lower bounds for mean estimation of Bernoulli products under general $\\\\ell_p$ losses, as well as tight bounds for mean estimation of Gaussian and sparse Gaussian distributions under the $\\\\ell_2$ loss.\",\"bibtex\":\"@inproceedings{DR19,\\n  title = \\t {Lower Bounds for Locally Private Estimation via Communication Complexity},\\n  author = \\t {Duchi, John and Rogers, Ryan},\\n  booktitle = \\t {32nd Conference on Learning Theory, {COLT} 2019},\\n  pages = \\t {1161--1191},\\n  year = \\t {2019},\\n  volume = \\t {99},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  publisher = \\t {PMLR},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DR19]</span> Develops a communication-complexity-based methodology for lower bounds under LDP constraints in the blackboard communication model. Obtains lower bounds for mean estimation of Bernoulli products under general $\\\\ell_p$ losses, as well as tight bounds for mean estimation of Gaussian and sparse Gaussian distributions under the $\\\\ell_2$ loss.}\\n }\\n\\n\",\"author_short\":[\"Duchi, J.\",\"Rogers, R.\"],\"key\":\"DR19\",\"id\":\"DR19\",\"bibbaseid\":\"duchi-rogers-lowerboundsforlocallyprivateestimationviacommunicationcomplexity-2019\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Memory, Communication, and Statistical Queries\",\"author\":[{\"firstnames\":[\"Jacob\"],\"propositions\":[],\"lastnames\":[\"Steinhardt\"],\"suffixes\":[]},{\"firstnames\":[\"Gregory\"],\"propositions\":[],\"lastnames\":[\"Valiant\"],\"suffixes\":[]},{\"firstnames\":[\"Stefan\"],\"propositions\":[],\"lastnames\":[\"Wager\"],\"suffixes\":[]}],\"pages\":\"1490–1516\",\"year\":\"2016\",\"editor\":[{\"firstnames\":[\"Vitaly\"],\"propositions\":[],\"lastnames\":[\"Feldman\"],\"suffixes\":[]},{\"firstnames\":[\"Alexander\"],\"propositions\":[],\"lastnames\":[\"Rakhlin\"],\"suffixes\":[]},{\"firstnames\":[\"Ohad\"],\"propositions\":[],\"lastnames\":[\"Shamir\"],\"suffixes\":[]}],\"volume\":\"49\",\"series\":\"Proceedings of Machine Learning Research\",\"address\":\"Columbia University, New York, New York, USA\",\"month\":\"23–26 Jun\",\"publisher\":\"PMLR\",\"url\":\"http://proceedings.mlr.press/v49/steinhardt16.html\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[SVW16]</span> Studies memory- and communication-constrained learning, and provides a general framework (based on statistical query (SQ) learning) to obtain lower bounds against those. Note that this allows to prove exponential separations for some problems (such as learning parities), but the reductions inherently lose polynomial factors.</div>\",\"bibtex\":\"@InProceedings{SVW16,\\n  title = \\t {Memory, Communication, and Statistical Queries},\\n  author = \\t {Jacob Steinhardt and Gregory Valiant and Stefan Wager},\\n  pages = \\t {1490--1516},\\n  year = \\t {2016},\\n  editor = \\t {Vitaly Feldman and Alexander Rakhlin and Ohad Shamir},\\n  volume = \\t {49},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  address = \\t {Columbia University, New York, New York, USA},\\n  month = \\t {23--26 Jun},\\n  publisher =    {PMLR},\\n  url = \\t {http://proceedings.mlr.press/v49/steinhardt16.html},\\n  bibbase_note = \\t {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[SVW16]</span> Studies memory- and communication-constrained learning, and provides a general framework (based on statistical query (SQ) learning) to obtain lower bounds against those. Note that this allows to prove exponential separations for some problems (such as learning parities), but the reductions inherently lose polynomial factors.</div>}\\n}\\n\",\"author_short\":[\"Steinhardt, J.\",\"Valiant, G.\",\"Wager, S.\"],\"editor_short\":[\"Feldman, V.\",\"Rakhlin, A.\",\"Shamir, O.\"],\"key\":\"SVW16\",\"id\":\"SVW16\",\"bibbaseid\":\"steinhardt-valiant-wager-memorycommunicationandstatisticalqueries-2016\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://proceedings.mlr.press/v49/steinhardt16.html\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Duchi\"],\"firstnames\":[\"John\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Jordan\"],\"firstnames\":[\"Michael\",\"I.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wainwright\"],\"firstnames\":[\"Martin\",\"J.\"],\"suffixes\":[]}],\"title\":\"Minimax optimal procedures for locally private estimation\",\"journal\":\"J. Amer. Statist. Assoc.\",\"fjournal\":\"Journal of the American Statistical Association\",\"volume\":\"113\",\"year\":\"2018\",\"number\":\"521\",\"pages\":\"182–201\",\"issn\":\"0162-1459\",\"mrclass\":\"62C20 (62B10 62D05 62G07 62J12)\",\"mrnumber\":\"3803452\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DJW18]</span> Results and techniques similar to those of [DJW13].</div>\",\"bibtex\":\"@article {DJW17,\\n    AUTHOR = {Duchi, John C. and Jordan, Michael I. and Wainwright, Martin\\n              J.},\\n     TITLE = {Minimax optimal procedures for locally private estimation},\\n   JOURNAL = {J. Amer. Statist. Assoc.},\\n  FJOURNAL = {Journal of the American Statistical Association},\\n    VOLUME = {113},\\n      YEAR = {2018},\\n    NUMBER = {521},\\n     PAGES = {182--201},\\n      ISSN = {0162-1459},\\n   MRCLASS = {62C20 (62B10 62D05 62G07 62J12)},\\n  MRNUMBER = {3803452},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[DJW18]</span> Results and techniques similar to those of [DJW13].</div>}\\n}\\n\\n\",\"author_short\":[\"Duchi, J. C.\",\"Jordan, M. I.\",\"Wainwright, M. J.\"],\"key\":\"DJW17\",\"id\":\"DJW17\",\"bibbaseid\":\"duchi-jordan-wainwright-minimaxoptimalproceduresforlocallyprivateestimation-2018\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"author\":[{\"firstnames\":[\"Ankit\"],\"propositions\":[],\"lastnames\":[\"Garg\"],\"suffixes\":[]},{\"firstnames\":[\"Tengyu\"],\"propositions\":[],\"lastnames\":[\"Ma\"],\"suffixes\":[]},{\"firstnames\":[\"Huy\",\"L.\"],\"propositions\":[],\"lastnames\":[\"Nguyen\"],\"suffixes\":[]}],\"title\":\"On Communication Cost of Distributed Statistical Estimation and Dimensionality\",\"booktitle\":\"Advances in Neural Information Processing Systems 27, NeurIPS'14\",\"pages\":\"2726–2734\",\"year\":\"2014\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[GMN14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols for various settings, specifically Gaussian mean estimation under $\\\\ell_2$ loss. Also incudes matching upper bounds in the blackboard model, which can be generalized to $\\\\ell_p$ in the sequentially interactive model.</div>\",\"bibtex\":\"@inproceedings{GMN14,\\n  author    = {Ankit Garg and\\n               Tengyu Ma and\\n               Huy L. Nguyen},\\n  title     = {On Communication Cost of Distributed Statistical Estimation and Dimensionality},\\n  booktitle = {Advances in Neural Information Processing Systems 27, {NeurIPS'14}},\\n  pages     = {2726--2734},\\n  year      = {2014},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[GMN14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols for various settings, specifically Gaussian mean estimation under $\\\\ell_2$ loss. Also incudes matching upper bounds in the blackboard model, which can be generalized to $\\\\ell_p$ in the sequentially interactive model.</div>}\\n}\\n\\n\",\"author_short\":[\"Garg, A.\",\"Ma, T.\",\"Nguyen, H. L.\"],\"key\":\"GMN14\",\"id\":\"GMN14\",\"bibbaseid\":\"garg-ma-nguyen-oncommunicationcostofdistributedstatisticalestimationanddimensionality-2014\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Pan-Private Uniformity Testing\",\"author\":[{\"firstnames\":[\"Kareem\"],\"propositions\":[],\"lastnames\":[\"Amin\"],\"suffixes\":[]},{\"firstnames\":[\"Matthew\"],\"propositions\":[],\"lastnames\":[\"Joseph\"],\"suffixes\":[]},{\"firstnames\":[\"Jieming\"],\"propositions\":[],\"lastnames\":[\"Mao\"],\"suffixes\":[]}],\"booktitle\":\"33rd Conference on Learning Theory, COLT 2020\",\"pages\":\"183–218\",\"year\":\"2020\",\"volume\":\"125\",\"series\":\"Proceedings of Machine Learning Research\",\"publisher\":\"PMLR\",\"pdf\":\"http://proceedings.mlr.press/v125/amin20a/amin20a.pdf\",\"url\":\"http://proceedings.mlr.press/v125/amin20a.html\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[AJM20]</span> Obtains, among others, tight lower bounds for uniformity testing (goodness-of-fit) under local privacy and pan-privacy (another version of differential privacy, \\\"in-between\\\" local and central DP) constraints. Those lower bounds apply to sequentially interactive protocols, and match the upper bounds from [ACFST20] (achieved by noninteractive, pubic-coin protocols).</div>\",\"bibtex\":\"@inproceedings{AJM20,\\n  title = \\t {Pan-Private Uniformity Testing},\\n  author = \\t {Kareem Amin and Matthew Joseph and Jieming Mao},\\n  booktitle = \\t {33rd Conference on Learning Theory, {COLT} 2020},\\n  pages = \\t {183--218},\\n  year = \\t {2020},\\n  volume = \\t {125},\\n  series = \\t {Proceedings of Machine Learning Research},\\n  publisher = \\t {PMLR},\\n  pdf = \\t {http://proceedings.mlr.press/v125/amin20a/amin20a.pdf},\\n  url = \\t {http://proceedings.mlr.press/v125/amin20a.html},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[AJM20]</span> Obtains, among others, tight lower bounds for uniformity testing (goodness-of-fit) under local privacy and pan-privacy (another version of differential privacy, \\\"in-between\\\" local and central DP) constraints. Those lower bounds apply to sequentially interactive protocols, and match the upper bounds from [ACFST20] (achieved by noninteractive, pubic-coin protocols).</div>}\\n}\\n\\n\",\"author_short\":[\"Amin, K.\",\"Joseph, M.\",\"Mao, J.\"],\"key\":\"AJM20\",\"id\":\"AJM20\",\"bibbaseid\":\"amin-joseph-mao-panprivateuniformitytesting-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://proceedings.mlr.press/v125/amin20a.html\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Kasiviswanathan\"],\"firstnames\":[\"Shiva\",\"Prasad\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lee\"],\"firstnames\":[\"Homin\",\"K.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Nissim\"],\"firstnames\":[\"Kobbi\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Raskhodnikova\"],\"firstnames\":[\"Sofya\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Smith\"],\"firstnames\":[\"Adam\"],\"suffixes\":[]}],\"title\":\"What can we learn privately?\",\"journal\":\"SIAM J. Comput.\",\"fjournal\":\"SIAM Journal on Computing\",\"volume\":\"40\",\"year\":\"2011\",\"number\":\"3\",\"pages\":\"793–826\",\"issn\":\"0097-5397\",\"mrclass\":\"68Q32\",\"mrnumber\":\"2823508\",\"mrreviewer\":\"Martin Anthony\",\"doi\":\"10.1137/090756090\",\"url\":\"https://doi.org/10.1137/090756090\",\"bibbase_note\":\"<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[KLNRS11]</span> Provides the first connection (and poly-factor equivalence) between learning under local privacy (LDP) constraints and statistical query (SQ) learning.</div>\",\"bibtex\":\"@article{KLNRS11,\\n    AUTHOR = {Kasiviswanathan, Shiva Prasad and Lee, Homin K. and Nissim,\\n              Kobbi and Raskhodnikova, Sofya and Smith, Adam},\\n     TITLE = {What can we learn privately?},\\n   JOURNAL = {SIAM J. Comput.},\\n  FJOURNAL = {SIAM Journal on Computing},\\n    VOLUME = {40},\\n      YEAR = {2011},\\n    NUMBER = {3},\\n     PAGES = {793--826},\\n      ISSN = {0097-5397},\\n   MRCLASS = {68Q32},\\n  MRNUMBER = {2823508},\\nMRREVIEWER = {Martin Anthony},\\n       DOI = {10.1137/090756090},\\n       URL = {https://doi.org/10.1137/090756090},\\n  bibbase_note = {<div class=\\\"well well-small bibbase\\\"><span class=\\\"bluecite\\\">[KLNRS11]</span> Provides the first connection (and poly-factor equivalence) between learning under local privacy (LDP) constraints and statistical query (SQ) learning.</div>}\\n}\\n\\n\",\"author_short\":[\"Kasiviswanathan, S. P.\",\"Lee, H. K.\",\"Nissim, K.\",\"Raskhodnikova, S.\",\"Smith, A.\"],\"key\":\"KLNRS11\",\"id\":\"KLNRS11\",\"bibbaseid\":\"kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1137/090756090\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"}],\n      metadata: {\"authorlinks\":{}},\n      ownerID: undefined\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"publications-annotated.bib\" href=\"data:text/bibtex;base64,@inproceedings{Feldman17,
  title = 	 {A General Characterization of the Statistical Query Complexity},
  author = 	 {Vitaly Feldman},
  pages = 	 {785--830},
  year = 	 {2017},
  editor = 	 {Satyen Kale and Ohad Shamir},
  volume = 	 {65},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Amsterdam, Netherlands},
  month = 	 {07--10 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v65/feldman17c/feldman17c.pdf},
  url = 	 {http://proceedings.mlr.press/v65/feldman17c.html},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[Feldman17]</span> Provides a characterization of SQ learning in terms of new "statistical dimension;" to be seen in view of the poly-factor equivalence between SQ learning and LDP-constrained/memory-constrained learnin (e.g., [KLNRS11,BDD98]). Includes applications to memory-limited streaming and communication-limited learning.</div>}
}
  


@article{GillR95,
    AUTHOR = {Gill, Richard D. and Levit, Boris Y.},
     TITLE = {Applications of the {V}an {T}rees inequality: a {B}ayesian
              {C}ram\'{e}r-{R}ao bound},
   JOURNAL = {Bernoulli},
  FJOURNAL = {Bernoulli. Official Journal of the Bernoulli Society for
              Mathematical Statistics and Probability},
    VOLUME = {1},
      YEAR = {1995},
    NUMBER = {1-2},
     PAGES = {59--79},
      ISSN = {1350-7265},
   MRCLASS = {62F10},
  MRNUMBER = {1354456},
MRREVIEWER = {V. K. Rohatgi},
       DOI = {10.2307/3318681},
       URL = {https://doi.org/10.2307/3318681},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[GL95]</span> Provides a good and self-contained primer and derivation of the van Trees inequality and its uses.</div>} 
}



@inproceedings{MMO19,
  author    = {Uri Meir and
               Dor Minzer and
               Rotem Oshman},
  title     = {Can Distributed Uniformity Testing Be Local?},
  booktitle = {2019 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2019},
  pages     = {228--237},
  publisher = {{ACM}},
  year      = {2019},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[MMO19]</span> Considers a similar setting as [FMO18], but allowing $\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\ell$-bit Boolean function.</div>}
}



@inproceedings{DGKR19,
  title = 	 {Communication and Memory Efficient Testing of Discrete Distributions},
  author = 	 {Diakonikolas, Ilias and Gouleakis, Themis and Kane, Daniel M. and Rao, Sankeerth},
  booktitle = 	 {32nd Conference on Learning Theory, {COLT} 2019},
  pages = 	 {1070--1106},
  year = 	 {2019},
  volume = 	 {99},
  series = 	 {Proceedings of Machine Learning Research},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v99/diakonikolas19a/diakonikolas19a.pdf},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[DGKR19]</span> Considers global memory constraints, in the blackboard model: the communication bound is for the total communication over all users, and as such the results are incomparable to works on local constraints, though some of the techniques can carry over. Establish tight or near-tight bounds for identity testing of discrete distributions; the techniques also apply to testing under memory constraints.</div>}
}



@inproceedings{BGMNW16,
  author    = {Mark Braverman and
               Ankit Garg and
               Tengyu Ma and
               Huy L. Nguyen and
               David P. Woodruff},
  title     = {Communication lower bounds for statistical estimation problems via
               a distributed data processing inequality},
  booktitle = {Symposium on Theory of Computing Conference, {STOC'16}},
  pages     = {1011--1020},
  publisher = {{ACM}},
  year      = {2016},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BGMNW16]</span> Significantly generalizes [GMN14], extending the lower bounds to the blackboard model, and the upper bounds to the SMP model. Includes tight results for sparse mean estimation. The lower bounds are obtained via a combination of strong data processing inequalities (SDPI) and the "cut-and-paste" property of Hellinger distance.</div>}
}



@inproceedings{Tsitsiklis93,
  title={Decentralized detection},
  author={Tsitsiklis, John N.},
  booktitle={Advances in Statistical Signal Processing},
  year={1993},
  volume = {2},
  editor = {H. V. Poor and J. B. Thomas},
  publisher = {JAI Press},
  pages = {297--344},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[Tsi93]</span> Considers <em>simple</em> hypothesis testing in a distributed setting, under communication constraints, and shows that for this problem public-coin (noninteractive) protocols are no more powerful than private-coin protocols.</div>}
}



@InProceedings{ACT20,
  title = 	 {Distributed Signal Detection under Communication Constraints},
  author =       {Acharya, Jayadev and Canonne, Cl{\'e}ment L. and Tyagi, Himanshu},
  pages = 	 {41--63},
  year = 	 {2020},
  volume = 	 {125},
  series = 	 {Proceedings of Machine Learning Research},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v125/acharya20b/acharya20b.pdf},
  url = 	 {http://proceedings.mlr.press/v125/acharya20b.html},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACT20c]</span> Applies the $χ^2$-contraction lower bound framework of [ACT20a] to obtain lower bounds for the problem of Gaussian mean testing (the hypothesis testing version of mean estimation in the Gaussian Location Model) under communication constraints (noninteractive). Also provides upper bounds for both private- and public-coin protocols.</div>}
}



@inproceedings{HMOW-ISIT18,
  author    = {Yanjun Han and Pritam Mukherjee and Ayfer {{\"O}zg{\"u}r} and Tsachy Weissman},
  title = {Distributed Statistical Estimation of High-Dimensional and Non-parametric Distributions},
  booktitle = {2018 IEEE International Symposium on Information Theory (ISIT'18)},
year = {2018},
pages={506--510},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[HMÖW18]</span> Lower bounds on distributed estimation (in total variation distance) of several families of distributions under communication constraints. Results apply to noniteractive protocols (a gap in the argument prevents the extension to interactive).</div>}
}



@inproceedings{FMO18,
  author    = {Orr Fischer and
               Uri Meir and
               Rotem Oshman},
  title     = {Distributed Uniformity Testing},
  booktitle = {2018 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2018},
  pages     = {455--464},
  publisher = {{ACM}},
  year      = {2018},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[FMO18]</span> Studies distributed uniformity testing in a setting where each user observe  multiple samples, and  communicates a single bit to the referee who  is  required  to  use a simple  aggregation rule, e.g., AND or a threshold. The goal is then to minimize the number of samples required per user. Also contains results on uniformity testing in other distributed models, such as the CONGEST or LOCAL models.</div>}
}



@inproceedings{ACHST20,
  title = 	 {Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit},
  author = 	 {Jayadev Acharya and Clément L Canonne and Yanjun Han and Ziteng Sun and Himanshu Tyagi},
  booktitle = 	 {33rd Conference on Learning Theory, {COLT} 2020},
  pages = 	 {3--40},
  year = 	 {2020},
  volume = 	 {125},
  series = 	 {Proceedings of Machine Learning Research},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v125/acharya20a/acharya20a.pdf},
  url = 	 {http://proceedings.mlr.press/v125/acharya20a.html},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACHST20]</span> Similar noninteractive setting as [ACT20a,ACT20b,ACFST20], for general local information constraints. Focus on the tight tradeoff between amount of public randomness available and sample complexity, for identity testing (goodness-of-fit).</div>}
}



@article{BCL20,
  author    = {S{\'{e}}bastien Bubeck and
               Sitan Chen and
               Jerry Li},
  title     = {Entanglement is Necessary for Optimal Quantum Property Testing},
  journal   = {CoRR},
  volume    = {abs/2004.07869},
  year      = {2020},
  note   = {To appear in FOCS'20.},
  url = {https://arxiv.org/abs/2004.07869},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BCL20]</span> Consider the task of testing whether a quantum state is maximally mixed vs. far from it in trace distance, given "local measurements" (no entanglement). Establishes a separation between non-adaptive (noninteractive) and adaptive (sequentially interactive) algorithms for this task. Even though this question does not, per se, fall under the same setting as distributed uniformity testing and the works are independent, the ideas bear resemblance to the $χ^2$-contraction lower bound framework of [ACT20a].</div>}
}



@inproceedings{BHO19,
  author    = {Leighton P. Barnes and
               Yanjun Han and
               Ayfer {\"{O}}zg{\"{u}}r},
  title     = {Fisher Information for Distributed Estimation under a Blackboard Communication Protocol},
  booktitle = {{ISIT}},
  pages     = {2704--2708},
  publisher = {{IEEE}},
  year      = {2019},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BHÖ19]</span> Provides general lower bounds for parameter estimation (and, in some cases, nonparametric density estimation) under $\ell_2$ loss for interactive protocols (blackboard model) under communication constraints, and instantiate it to obtain tight bounds for various statistical models such as Gaussian, product Bernoulli, and discrete distribution estimation. At its core, the lower bounds rely on a Cramér–Rao/van Trees-type approach, which leaves the (trace of) the Fisher information matrix as quantity to analyze to get lower bounds.</div>}
}



@article{BCO20,
  author    = {Leighton P. Barnes and
               Wei{-}Ning Chen and
               Ayfer {\"{O}}zg{\"{u}}r},
  title     = {Fisher information under local differential privacy},
  journal   = {CoRR},
  volume    = {abs/2005.10783},
  url = {https://arxiv.org/abs/2005.10783},
  year      = {2020},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BCÖ20]</span> Provides lower bounds for parameter estimation under $\ell_2$ loss for interactive protocols (blackboard model) under local privacy, and instantiate it to obtain tight bounds for Gaussian mean estimation, (sparse) Bernoulli mean estimation, and discrete distribution estimation. As in [BHÖ19], the lower bound framework is based on a Cramér–Rao/van Trees-type approach.},
  note = {Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT).</div>}
}



@inproceedings{Shamir14,
  title={Fundamental limits of online and distributed algorithms for statistical learning and estimation},
  author={Shamir, Ohad},
  booktitle= {Advances in Neural Information Processing Systems 27, {NeurIPS'14}},
  pages={163--171},
  year={2014},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[Sha14]</span> Considers estimation tasks under various information constraints, such as memory or communication. Establishes results for sequentially interactive protocols for those problems by proving a lower bound on the "hide-and-seek" problem, that is, the mean estimation problem for high-dimensional product Bernoulli distributions with 1-sparse mean vectors.</div>}
}



@article{ACT20:HD,
  author    = {Jayadev Acharya and
               Cl{\'{e}}ment L. Canonne and
               Himanshu Tyagi},
  title     = {General lower bounds for interactive high-dimensional estimation under
               information constraints},
  journal   = {CoRR},
  volume    = {abs/2010.06562},
  year      = {2020},
  url = {https://arxiv.org/abs/2010.06562},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACT20d]</span> Abstracts and generalizes the lower bound framework of [ACLST20] to provide "plug-and-play" lower bounds for parameter estimation with sequentially interactive protocolunder general information constraints. Instantiates them to get lower bounds for $\ell_p$ losses in the cases of discrete distribution estimation, Gaussian mean estimation, and product Bernoulli mean estimation; and complements them with upper bounds.</div>}
}



@inproceedings{HOW18,
  author    = {Yanjun Han and
               Ayfer {\"{O}}zg{\"{u}}r and
               Tsachy Weissman},
  title     = {Geometric Lower Bounds for Distributed Parameter Estimation under
               Communication Constraints},
  booktitle = {31st Conference on Learning Theory, {COLT} 2018},
  series    = {Proceedings of Machine Learning Research},
  volume    = {75},
  pages     = {3163--3188},
  publisher = {{PMLR}},
  year      = {2018},
  note = {See updated version, \url{https://arxiv.org/abs/1802.08417v3} (2020).},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[HÖW18]</span> Lower bounds on distributed parameter estimation under the $\ell_2$ loss of several families of distributions, including high-dimensional, under communication constraints. Results for the latest version, using techniques similar to those of [ACLST20,ACT20d], extend to the blackboard model and include $\ell_p$ losses.</div>}
}



@article{ACT19:LB,
  title = 	 {Inference under Information Constraints {I}: Lower Bounds from Chi-Square Contraction},
  author = 	 {Acharya, Jayadev and Canonne, Cl{\'{e}}ment L. and Tyagi, Himanshu},
  journal = 	 {IEEE Transactions on Information Theory},
  year = 	 {2020},
  note = {Conference version in {COLT'19}},
  url = {https://arxiv.org/abs/1812.11476},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACT20a]</span> Provides a unified lower bound framework to derive sample complexity lower bounds for noninteractive protocols under general local information constraints, captured by a characterization of $\mathcal{W}$ in terms of various norms of a p.s.d. matrix $H(W)$.</div>}
}



@article{ACT19:UB,
  title = 	 {Inference under Information Constraints {II}: Communication Constraints and Shared Randomness},
  author = 	 {Acharya, Jayadev and Canonne, Cl{\'{e}}ment L. and Tyagi, Himanshu},
  journal = {IEEE Transactions on Information Theory},
  year = 	 {2020},
  note = {Conference version in {ICML'19}},
  url = {https://arxiv.org/abs/1905.08302},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACT20b]</span> Focuses on the communication constraints ($\ell$ bits per player), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a].</div>}
}



@misc{ACFST19,
  author    = {Jayadev Acharya and
               Cl{\'{e}}ment L. Canonne and
              Cody Freitag and Ziteng Sun
              and Himanshu Tyagi},
  title     = {Inference under Information Constraints {III}: Local Privacy Constraints},
  note = {Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT). Preprint available at arXiv:abs/1808.02174; Conference version in {AISTATS'19}},
  year      = {2020},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACFST20]</span> Focuses on the local privacy constraints (ρ-LDP), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a]. Also contains lower bounds for independence testing under LDP.</div>}
}



@inproceedings{ZDJW13,
  title={Information-theoretic lower bounds for distributed statistical estimation with communication constraints},
  author={Zhang, Yuchen and Duchi, John and Jordan, Michael I. and Wainwright, Martin J.},
  booktitle= {Advances in Neural Information Processing Systems 26, {NeurIPS'13}},
  pages={2328--2336},
  year={2013},
  url = {https://arxiv.org/abs/1405.0782},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ZDJW13]</span> and <span class="bluecite">[DJWZ14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols  under communication constraints under $\ell_2$ loss for various estimation problems, including Gaussian and Bernoulli mean estimation. Also includes some results for interactive protocols.</div>}
}



@article{ACLST20,
  author    = {Jayadev Acharya and
               Cl{\'{e}}ment L. Canonne and
               Yuhan Liu and
               Ziteng Sun and
               Himanshu Tyagi},
  title     = {Interactive Inference under Information Constraints},
  journal   = {CoRR},
  volume    = {abs/2007.10976},
  year      = {2020},
  url       = {https://arxiv.org/abs/2007.10976},
  archivePrefix = {arXiv},
  eprint    = {2007.10976},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[ACLST20]</span> Focuses on density estimation (learning) and goodness-of-fit (identity testing) of discrete distributions with regard to total variation ($\ell_1$ metric), for sequentially interactive protocols under general local information constraints. Implies tight bounds for those problems under LDP and communication constraints.</div>}
}



@article{BenDavidD98,
    AUTHOR = {Ben-David, Shai and Dichterman, Eli},
     TITLE = {Learning with restricted focus of attention},
   JOURNAL = {J. Comput. System Sci.},
  FJOURNAL = {Journal of Computer and System Sciences},
    VOLUME = {56},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {277--298},
      ISSN = {0022-0000},
   MRCLASS = {68Q32 (68T05)},
  MRNUMBER = {1633977},
       DOI = {10.1006/jcss.1998.1569},
       URL = {https://doi.org/10.1006/jcss.1998.1569},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BDD98]</span> Provides the first connection (and poly-factor equivalence) between learning with communication constraints (wRFA: "restricted focus of attention'') and statistical query (SQ) learning.</div>}
}



@inproceedings{DJW13:FOCS,
  author    = {John C. Duchi and
               Michael I. Jordan and
               Martin J. Wainwright},
  title     = {Local Privacy and Statistical Minimax Rates},
  booktitle = focs13,
  pages     = {429--438},
  publisher = {{IEEE} Computer Society},
  year      = {2013},
  note = {Full version at \url{https://arxiv.org/abs/1302.3203}.},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[DJW13]</span> Lower bounds on parameter estimation for several families of distributions under LDP constraints, via strong data processing inequalities (SDPI) and a locally private version of Le Cam, Fano, and Assouad's lemmata. Results apply to the one-dimensional setting, and in high dimensions for noninteractive protocols.</div>}
}



@article{BB20,
    title={Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms},
    author={Thomas B. Berrett and Cristina Butucea},
    journal = {CoRR},
    year={2020},
    volume    = {abs/2005.12601},
    note = {To appear in {NeurIPS'20}.},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BB20]</span> Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\mathbf{q}$ (while the other two works focus on the worst-case $\mathbf{q}$, i.e., the uniform distribution).</div>}
}



@inproceedings{DR19,
  title = 	 {Lower Bounds for Locally Private Estimation via Communication Complexity},
  author = 	 {Duchi, John and Rogers, Ryan},
  booktitle = 	 {32nd Conference on Learning Theory, {COLT} 2019},
  pages = 	 {1161--1191},
  year = 	 {2019},
  volume = 	 {99},
  series = 	 {Proceedings of Machine Learning Research},
  publisher = 	 {PMLR},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[DR19]</span> Develops a communication-complexity-based methodology for lower bounds under LDP constraints in the blackboard communication model. Obtains lower bounds for mean estimation of Bernoulli products under general $\ell_p$ losses, as well as tight bounds for mean estimation of Gaussian and sparse Gaussian distributions under the $\ell_2$ loss.}
 }



@InProceedings{SVW16,
  title = 	 {Memory, Communication, and Statistical Queries},
  author = 	 {Jacob Steinhardt and Gregory Valiant and Stefan Wager},
  pages = 	 {1490--1516},
  year = 	 {2016},
  editor = 	 {Vitaly Feldman and Alexander Rakhlin and Ohad Shamir},
  volume = 	 {49},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Columbia University, New York, New York, USA},
  month = 	 {23--26 Jun},
  publisher =    {PMLR},
  url = 	 {http://proceedings.mlr.press/v49/steinhardt16.html},
  bibbase_note = 	 {<div class="well well-small bibbase"><span class="bluecite">[SVW16]</span> Studies memory- and communication-constrained learning, and provides a general framework (based on statistical query (SQ) learning) to obtain lower bounds against those. Note that this allows to prove exponential separations for some problems (such as learning parities), but the reductions inherently lose polynomial factors.</div>}
}


@article {DJW17,
    AUTHOR = {Duchi, John C. and Jordan, Michael I. and Wainwright, Martin
              J.},
     TITLE = {Minimax optimal procedures for locally private estimation},
   JOURNAL = {J. Amer. Statist. Assoc.},
  FJOURNAL = {Journal of the American Statistical Association},
    VOLUME = {113},
      YEAR = {2018},
    NUMBER = {521},
     PAGES = {182--201},
      ISSN = {0162-1459},
   MRCLASS = {62C20 (62B10 62D05 62G07 62J12)},
  MRNUMBER = {3803452},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[DJW18]</span> Results and techniques similar to those of [DJW13].</div>}
}



@inproceedings{GMN14,
  author    = {Ankit Garg and
               Tengyu Ma and
               Huy L. Nguyen},
  title     = {On Communication Cost of Distributed Statistical Estimation and Dimensionality},
  booktitle = {Advances in Neural Information Processing Systems 27, {NeurIPS'14}},
  pages     = {2726--2734},
  year      = {2014},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[GMN14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols for various settings, specifically Gaussian mean estimation under $\ell_2$ loss. Also incudes matching upper bounds in the blackboard model, which can be generalized to $\ell_p$ in the sequentially interactive model.</div>}
}



@inproceedings{AJM20,
  title = 	 {Pan-Private Uniformity Testing},
  author = 	 {Kareem Amin and Matthew Joseph and Jieming Mao},
  booktitle = 	 {33rd Conference on Learning Theory, {COLT} 2020},
  pages = 	 {183--218},
  year = 	 {2020},
  volume = 	 {125},
  series = 	 {Proceedings of Machine Learning Research},
  publisher = 	 {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v125/amin20a/amin20a.pdf},
  url = 	 {http://proceedings.mlr.press/v125/amin20a.html},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[AJM20]</span> Obtains, among others, tight lower bounds for uniformity testing (goodness-of-fit) under local privacy and pan-privacy (another version of differential privacy, "in-between" local and central DP) constraints. Those lower bounds apply to sequentially interactive protocols, and match the upper bounds from [ACFST20] (achieved by noninteractive, pubic-coin protocols).</div>}
}



@article{KLNRS11,
    AUTHOR = {Kasiviswanathan, Shiva Prasad and Lee, Homin K. and Nissim,
              Kobbi and Raskhodnikova, Sofya and Smith, Adam},
     TITLE = {What can we learn privately?},
   JOURNAL = {SIAM J. Comput.},
  FJOURNAL = {SIAM Journal on Computing},
    VOLUME = {40},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {793--826},
      ISSN = {0097-5397},
   MRCLASS = {68Q32},
  MRNUMBER = {2823508},
MRREVIEWER = {Martin Anthony},
       DOI = {10.1137/090756090},
       URL = {https://doi.org/10.1137/090756090},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[KLNRS11]</span> Provides the first connection (and poly-factor equivalence) between learning under local privacy (LDP) constraints and statistical query (SQ) learning.</div>}
}

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Canonne;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n  In volume 125, of <i>Proceedings of Machine Learning Research</i>, pages 41–63,  2020. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACT20c]</span> Applies the $χ^2$-contraction lower bound framework of [ACT20a] to obtain lower bounds for the problem of Gaussian mean testing (the hypothesis testing version of mean estimation in the Gaussian Location Model) under communication constraints (noninteractive). Also provides upper bounds for both private- and public-coin protocols.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://proceedings.mlr.press/v125/acharya20b.html\"\n     onclick=\"log_download('acharya-canonne-tyagi-distributedsignaldetectionundercommunicationconstraints-2020', 'http://proceedings.mlr.press/v125/acharya20b.html', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Distributed Signal Detection under Communication Constraints [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-tyagi-distributedsignaldetectionundercommunicationconstraints-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>21 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-tyagi-distributedsignaldetectionundercommunicationconstraints-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@InProceedings{ACT20,\n  title = \t {Distributed Signal Detection under Communication Constraints},\n  author =       {Acharya, Jayadev and Canonne, Cl{\\&#x27;e}ment L. and Tyagi, Himanshu},\n  pages = \t {41--63},\n  year = \t {2020},\n  volume = \t {125},\n  series = \t {Proceedings of Machine Learning Research},\n  publisher =    {PMLR},\n  pdf = \t {http://proceedings.mlr.press/v125/acharya20b/acharya20b.pdf},\n  url = \t {http://proceedings.mlr.press/v125/acharya20b.html},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACT20c]&lt;/span&gt; Applies the $χ^2$-contraction lower bound framework of [ACT20a] to obtain lower bounds for the problem of Gaussian mean testing (the hypothesis testing version of mean estimation in the Gaussian Location Model) under communication constraints (noninteractive). Also provides upper bounds for both private- and public-coin protocols.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"acharya-canonne-han-sun-tyagi-domaincompressionanditsapplicationtorandomnessoptimaldistributedgoodnessoffit-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://proceedings.mlr.press/v125/acharya20a.html\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'acharya-canonne-han-sun-tyagi-domaincompressionanditsapplicationtorandomnessoptimaldistributedgoodnessoffit-2020', 'http://proceedings.mlr.press/v125/acharya20a.html', event);\">\n    Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jayadev Acharya;  Clément L Canonne;  Yanjun Han;  Ziteng Sun;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n  In <i>33rd Conference on Learning Theory, COLT 2020</i>, volume 125, of <i>Proceedings of Machine Learning Research</i>, pages 3–40,  2020. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACHST20]</span> Similar noninteractive setting as [ACT20a,ACT20b,ACFST20], for general local information constraints. Focus on the tight tradeoff between amount of public randomness available and sample complexity, for identity testing (goodness-of-fit).</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://proceedings.mlr.press/v125/acharya20a.html\"\n     onclick=\"log_download('acharya-canonne-han-sun-tyagi-domaincompressionanditsapplicationtorandomnessoptimaldistributedgoodnessoffit-2020', 'http://proceedings.mlr.press/v125/acharya20a.html', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-han-sun-tyagi-domaincompressionanditsapplicationtorandomnessoptimaldistributedgoodnessoffit-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>62 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-han-sun-tyagi-domaincompressionanditsapplicationtorandomnessoptimaldistributedgoodnessoffit-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{ACHST20,\n  title = \t {Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit},\n  author = \t {Jayadev Acharya and Clément L Canonne and Yanjun Han and Ziteng Sun and Himanshu Tyagi},\n  booktitle = \t {33rd Conference on Learning Theory, {COLT} 2020},\n  pages = \t {3--40},\n  year = \t {2020},\n  volume = \t {125},\n  series = \t {Proceedings of Machine Learning Research},\n  publisher = \t {PMLR},\n  pdf = \t {http://proceedings.mlr.press/v125/acharya20a/acharya20a.pdf},\n  url = \t {http://proceedings.mlr.press/v125/acharya20a.html},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACHST20]&lt;/span&gt; Similar noninteractive setting as [ACT20a,ACT20b,ACFST20], for general local information constraints. Focus on the tight tradeoff between amount of public randomness available and sample complexity, for identity testing (goodness-of-fit).&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"bubeck-chen-li-entanglementisnecessaryforoptimalquantumpropertytesting-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2004.07869\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'bubeck-chen-li-entanglementisnecessaryforoptimalquantumpropertytesting-2020', 'https://arxiv.org/abs/2004.07869', event);\">\n    Entanglement is Necessary for Optimal Quantum Property Testing.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Sébastien Bubeck;  Sitan Chen;  and  Jerry Li.\n</span>\n\n  \n\n</span>\n\n  <i>CoRR</i>, abs/2004.07869.  2020.\n  <span class=\"note\">To appear in FOCS'20.</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[BCL20]</span> Consider the task of testing whether a quantum state is maximally mixed vs. far from it in trace distance, given \"local measurements\" (no entanglement). Establishes a separation between non-adaptive (noninteractive) and adaptive (sequentially interactive) algorithms for this task. Even though this question does not, per se, fall under the same setting as distributed uniformity testing and the works are independent, the ideas bear resemblance to the $χ^2$-contraction lower bound framework of [ACT20a].</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/2004.07869\"\n     onclick=\"log_download('bubeck-chen-li-entanglementisnecessaryforoptimalquantumpropertytesting-2020', 'https://arxiv.org/abs/2004.07869', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Entanglement is Necessary for Optimal Quantum Property Testing [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/bubeck-chen-li-entanglementisnecessaryforoptimalquantumpropertytesting-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('bubeck-chen-li-entanglementisnecessaryforoptimalquantumpropertytesting-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{BCL20,\n  author    = {S{\\&#x27;{e}}bastien Bubeck and\n               Sitan Chen and\n               Jerry Li},\n  title     = {Entanglement is Necessary for Optimal Quantum Property Testing},\n  journal   = {CoRR},\n  volume    = {abs/2004.07869},\n  year      = {2020},\n  note   = {To appear in FOCS&#x27;20.},\n  url = {https://arxiv.org/abs/2004.07869},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[BCL20]&lt;/span&gt; Consider the task of testing whether a quantum state is maximally mixed vs. far from it in trace distance, given &quot;local measurements&quot; (no entanglement). Establishes a separation between non-adaptive (noninteractive) and adaptive (sequentially interactive) algorithms for this task. Even though this question does not, per se, fall under the same setting as distributed uniformity testing and the works are independent, the ideas bear resemblance to the $χ^2$-contraction lower bound framework of [ACT20a].&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"barnes-chen-zgr-fisherinformationunderlocaldifferentialprivacy-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2005.10783\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'barnes-chen-zgr-fisherinformationunderlocaldifferentialprivacy-2020', 'https://arxiv.org/abs/2005.10783', event);\">\n    Fisher information under local differential privacy.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Leighton P. Barnes;  Wei-Ning Chen;  and  Ayfer Özgür.\n</span>\n\n  \n\n</span>\n\n  <i>CoRR</i>, abs/2005.10783.  2020.\n  <span class=\"note\">Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT).</div></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[BCÖ20]</span> Provides lower bounds for parameter estimation under $\\ell_2$ loss for interactive protocols (blackboard model) under local privacy, and instantiate it to obtain tight bounds for Gaussian mean estimation, (sparse) Bernoulli mean estimation, and discrete distribution estimation. As in [BHÖ19], the lower bound framework is based on a Cramér–Rao/van Trees-type approach.</span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/2005.10783\"\n     onclick=\"log_download('barnes-chen-zgr-fisherinformationunderlocaldifferentialprivacy-2020', 'https://arxiv.org/abs/2005.10783', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Fisher information under local differential privacy [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/barnes-chen-zgr-fisherinformationunderlocaldifferentialprivacy-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('barnes-chen-zgr-fisherinformationunderlocaldifferentialprivacy-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{BCO20,\n  author    = {Leighton P. Barnes and\n               Wei{-}Ning Chen and\n               Ayfer {\\&quot;{O}}zg{\\&quot;{u}}r},\n  title     = {Fisher information under local differential privacy},\n  journal   = {CoRR},\n  volume    = {abs/2005.10783},\n  url = {https://arxiv.org/abs/2005.10783},\n  year      = {2020},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[BCÖ20]&lt;/span&gt; Provides lower bounds for parameter estimation under $\\ell_2$ loss for interactive protocols (blackboard model) under local privacy, and instantiate it to obtain tight bounds for Gaussian mean estimation, (sparse) Bernoulli mean estimation, and discrete distribution estimation. As in [BHÖ19], the lower bound framework is based on a Cramér–Rao/van Trees-type approach.},\n  note = {Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT).&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"acharya-canonne-tyagi-generallowerboundsforinteractivehighdimensionalestimationunderinformationconstraints-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2010.06562\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'acharya-canonne-tyagi-generallowerboundsforinteractivehighdimensionalestimationunderinformationconstraints-2020', 'https://arxiv.org/abs/2010.06562', event);\">\n    General lower bounds for interactive high-dimensional estimation under information constraints.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jayadev Acharya;  Clément L. Canonne;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n  <i>CoRR</i>, abs/2010.06562.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACT20d]</span> Abstracts and generalizes the lower bound framework of [ACLST20] to provide \"plug-and-play\" lower bounds for parameter estimation with sequentially interactive protocolunder general information constraints. Instantiates them to get lower bounds for $\\ell_p$ losses in the cases of discrete distribution estimation, Gaussian mean estimation, and product Bernoulli mean estimation; and complements them with upper bounds.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/2010.06562\"\n     onclick=\"log_download('acharya-canonne-tyagi-generallowerboundsforinteractivehighdimensionalestimationunderinformationconstraints-2020', 'https://arxiv.org/abs/2010.06562', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"General lower bounds for interactive high-dimensional estimation under information constraints [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-tyagi-generallowerboundsforinteractivehighdimensionalestimationunderinformationconstraints-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>65 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-tyagi-generallowerboundsforinteractivehighdimensionalestimationunderinformationconstraints-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{ACT20:HD,\n  author    = {Jayadev Acharya and\n               Cl{\\&#x27;{e}}ment L. Canonne and\n               Himanshu Tyagi},\n  title     = {General lower bounds for interactive high-dimensional estimation under\n               information constraints},\n  journal   = {CoRR},\n  volume    = {abs/2010.06562},\n  year      = {2020},\n  url = {https://arxiv.org/abs/2010.06562},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACT20d]&lt;/span&gt; Abstracts and generalizes the lower bound framework of [ACLST20] to provide &quot;plug-and-play&quot; lower bounds for parameter estimation with sequentially interactive protocolunder general information constraints. Instantiates them to get lower bounds for $\\ell_p$ losses in the cases of discrete distribution estimation, Gaussian mean estimation, and product Bernoulli mean estimation; and complements them with upper bounds.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"acharya-canonne-tyagi-inferenceunderinformationconstraintsilowerboundsfromchisquarecontraction-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1812.11476\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'acharya-canonne-tyagi-inferenceunderinformationconstraintsilowerboundsfromchisquarecontraction-2020', 'https://arxiv.org/abs/1812.11476', event);\">\n    Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jayadev Acharya;  Clément L. Canonne;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Transactions on Information Theory</i>.  2020.\n  <span class=\"note\">Conference version in COLT'19</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACT20a]</span> Provides a unified lower bound framework to derive sample complexity lower bounds for noninteractive protocols under general local information constraints, captured by a characterization of $\\mathcal{W}$ in terms of various norms of a p.s.d. matrix $H(W)$.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1812.11476\"\n     onclick=\"log_download('acharya-canonne-tyagi-inferenceunderinformationconstraintsilowerboundsfromchisquarecontraction-2020', 'https://arxiv.org/abs/1812.11476', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-tyagi-inferenceunderinformationconstraintsilowerboundsfromchisquarecontraction-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>70 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-tyagi-inferenceunderinformationconstraintsilowerboundsfromchisquarecontraction-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{ACT19:LB,\n  title = \t {Inference under Information Constraints {I}: Lower Bounds from Chi-Square Contraction},\n  author = \t {Acharya, Jayadev and Canonne, Cl{\\&#x27;{e}}ment L. and Tyagi, Himanshu},\n  journal = \t {IEEE Transactions on Information Theory},\n  year = \t {2020},\n  note = {Conference version in {COLT&#x27;19}},\n  url = {https://arxiv.org/abs/1812.11476},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACT20a]&lt;/span&gt; Provides a unified lower bound framework to derive sample complexity lower bounds for noninteractive protocols under general local information constraints, captured by a characterization of $\\mathcal{W}$ in terms of various norms of a p.s.d. matrix $H(W)$.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"acharya-canonne-tyagi-inferenceunderinformationconstraintsiicommunicationconstraintsandsharedrandomness-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1905.08302\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'acharya-canonne-tyagi-inferenceunderinformationconstraintsiicommunicationconstraintsandsharedrandomness-2020', 'https://arxiv.org/abs/1905.08302', event);\">\n    Inference under Information Constraints II: Communication Constraints and Shared Randomness.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jayadev Acharya;  Clément L. Canonne;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Transactions on Information Theory</i>.  2020.\n  <span class=\"note\">Conference version in ICML'19</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACT20b]</span> Focuses on the communication constraints ($\\ell$ bits per player), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a].</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1905.08302\"\n     onclick=\"log_download('acharya-canonne-tyagi-inferenceunderinformationconstraintsiicommunicationconstraintsandsharedrandomness-2020', 'https://arxiv.org/abs/1905.08302', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Inference under Information Constraints II: Communication Constraints and Shared Randomness [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-tyagi-inferenceunderinformationconstraintsiicommunicationconstraintsandsharedrandomness-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>44 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-tyagi-inferenceunderinformationconstraintsiicommunicationconstraintsandsharedrandomness-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{ACT19:UB,\n  title = \t {Inference under Information Constraints {II}: Communication Constraints and Shared Randomness},\n  author = \t {Acharya, Jayadev and Canonne, Cl{\\&#x27;{e}}ment L. and Tyagi, Himanshu},\n  journal = {IEEE Transactions on Information Theory},\n  year = \t {2020},\n  note = {Conference version in {ICML&#x27;19}},\n  url = {https://arxiv.org/abs/1905.08302},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACT20b]&lt;/span&gt; Focuses on the communication constraints ($\\ell$ bits per player), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a].&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"acharya-canonne-freitag-sun-tyagi-inferenceunderinformationconstraintsiiilocalprivacyconstraints-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Inference under Information Constraints III: Local Privacy Constraints.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jayadev Acharya;  Clément L. Canonne;  Cody Freitag;  Ziteng Sun;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n   2020.\n  <span class=\"note\">Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT). Preprint available at arXiv:abs/1808.02174; Conference version in AISTATS'19</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACFST20]</span> Focuses on the local privacy constraints (ρ-LDP), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a]. Also contains lower bounds for independence testing under LDP.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-freitag-sun-tyagi-inferenceunderinformationconstraintsiiilocalprivacyconstraints-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-freitag-sun-tyagi-inferenceunderinformationconstraintsiiilocalprivacyconstraints-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{ACFST19,\n  author    = {Jayadev Acharya and\n               Cl{\\&#x27;{e}}ment L. Canonne and\n              Cody Freitag and Ziteng Sun\n              and Himanshu Tyagi},\n  title     = {Inference under Information Constraints {III}: Local Privacy Constraints},\n  note = {Accepted to the IEEE Journal on Selected Areas in Information Theory (JSAIT). Preprint available at arXiv:abs/1808.02174; Conference version in {AISTATS&#x27;19}},\n  year      = {2020},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACFST20]&lt;/span&gt; Focuses on the local privacy constraints (ρ-LDP), and provides public- and private-coin protocols for identity testing, and private-coin protocols for learning which match the lower bounds from [ACT20a]. Also contains lower bounds for independence testing under LDP.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"acharya-canonne-liu-sun-tyagi-interactiveinferenceunderinformationconstraints-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2007.10976\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'acharya-canonne-liu-sun-tyagi-interactiveinferenceunderinformationconstraints-2020', 'https://arxiv.org/abs/2007.10976', event);\">\n    Interactive Inference under Information Constraints.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jayadev Acharya;  Clément L. Canonne;  Yuhan Liu;  Ziteng Sun;  and  Himanshu Tyagi.\n</span>\n\n  \n\n</span>\n\n  <i>CoRR</i>, abs/2007.10976.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ACLST20]</span> Focuses on density estimation (learning) and goodness-of-fit (identity testing) of discrete distributions with regard to total variation ($\\ell_1$ metric), for sequentially interactive protocols under general local information constraints. Implies tight bounds for those problems under LDP and communication constraints.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/2007.10976\"\n     onclick=\"log_download('acharya-canonne-liu-sun-tyagi-interactiveinferenceunderinformationconstraints-2020', 'https://arxiv.org/abs/2007.10976', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Interactive Inference under Information Constraints [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-canonne-liu-sun-tyagi-interactiveinferenceunderinformationconstraints-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>23 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-canonne-liu-sun-tyagi-interactiveinferenceunderinformationconstraints-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{ACLST20,\n  author    = {Jayadev Acharya and\n               Cl{\\&#x27;{e}}ment L. Canonne and\n               Yuhan Liu and\n               Ziteng Sun and\n               Himanshu Tyagi},\n  title     = {Interactive Inference under Information Constraints},\n  journal   = {CoRR},\n  volume    = {abs/2007.10976},\n  year      = {2020},\n  url       = {https://arxiv.org/abs/2007.10976},\n  archivePrefix = {arXiv},\n  eprint    = {2007.10976},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ACLST20]&lt;/span&gt; Focuses on density estimation (learning) and goodness-of-fit (identity testing) of discrete distributions with regard to total variation ($\\ell_1$ metric), for sequentially interactive protocols under general local information constraints. Implies tight bounds for those problems under LDP and communication constraints.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"berrett-butucea-locallyprivatenonasymptotictestingofdiscretedistributionsisfasterusinginteractivemechanisms-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Thomas B. Berrett;  and  Cristina Butucea.\n</span>\n\n  \n\n</span>\n\n  <i>CoRR</i>, abs/2005.12601.  2020.\n  <span class=\"note\">To appear in NeurIPS'20.</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[BB20]</span> Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\\mathbf{q}$ (while the other two works focus on the worst-case $\\mathbf{q}$, i.e., the uniform distribution).</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/berrett-butucea-locallyprivatenonasymptotictestingofdiscretedistributionsisfasterusinginteractivemechanisms-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('berrett-butucea-locallyprivatenonasymptotictestingofdiscretedistributionsisfasterusinginteractivemechanisms-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{BB20,\n    title={Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms},\n    author={Thomas B. Berrett and Cristina Butucea},\n    journal = {CoRR},\n    year={2020},\n    volume    = {abs/2005.12601},\n    note = {To appear in {NeurIPS&#x27;20}.},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[BB20]&lt;/span&gt; Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\\mathbf{q}$ (while the other two works focus on the worst-case $\\mathbf{q}$, i.e., the uniform distribution).&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"amin-joseph-mao-panprivateuniformitytesting-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://proceedings.mlr.press/v125/amin20a.html\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'amin-joseph-mao-panprivateuniformitytesting-2020', 'http://proceedings.mlr.press/v125/amin20a.html', event);\">\n    Pan-Private Uniformity Testing.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Kareem Amin;  Matthew Joseph;  and  Jieming Mao.\n</span>\n\n  \n\n</span>\n\n  In <i>33rd Conference on Learning Theory, COLT 2020</i>, volume 125, of <i>Proceedings of Machine Learning Research</i>, pages 183–218,  2020. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[AJM20]</span> Obtains, among others, tight lower bounds for uniformity testing (goodness-of-fit) under local privacy and pan-privacy (another version of differential privacy, \"in-between\" local and central DP) constraints. Those lower bounds apply to sequentially interactive protocols, and match the upper bounds from [ACFST20] (achieved by noninteractive, pubic-coin protocols).</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://proceedings.mlr.press/v125/amin20a.html\"\n     onclick=\"log_download('amin-joseph-mao-panprivateuniformitytesting-2020', 'http://proceedings.mlr.press/v125/amin20a.html', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Pan-Private Uniformity Testing [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/amin-joseph-mao-panprivateuniformitytesting-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('amin-joseph-mao-panprivateuniformitytesting-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{AJM20,\n  title = \t {Pan-Private Uniformity Testing},\n  author = \t {Kareem Amin and Matthew Joseph and Jieming Mao},\n  booktitle = \t {33rd Conference on Learning Theory, {COLT} 2020},\n  pages = \t {183--218},\n  year = \t {2020},\n  volume = \t {125},\n  series = \t {Proceedings of Machine Learning Research},\n  publisher = \t {PMLR},\n  pdf = \t {http://proceedings.mlr.press/v125/amin20a/amin20a.pdf},\n  url = \t {http://proceedings.mlr.press/v125/amin20a.html},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[AJM20]&lt;/span&gt; Obtains, among others, tight lower bounds for uniformity testing (goodness-of-fit) under local privacy and pan-privacy (another version of differential privacy, &quot;in-between&quot; local and central DP) constraints. Those lower bounds apply to sequentially interactive protocols, and match the upper bounds from [ACFST20] (achieved by noninteractive, pubic-coin protocols).&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2019\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2019')\"\n      onkeypress=\"toggleGroup('group_2019')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2019</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"meir-minzer-oshman-candistributeduniformitytestingbelocal-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Can Distributed Uniformity Testing Be Local?.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Uri Meir;  Dor Minzer;  and  Rotem Oshman.\n</span>\n\n  \n\n</span>\n\n  In <i>2019 ACM Symposium on Principles of Distributed Computing, PODC 2019</i>, pages 228–237,  2019. ACM\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[MMO19]</span> Considers a similar setting as [FMO18], but allowing $\\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\\ell$-bit Boolean function.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/meir-minzer-oshman-candistributeduniformitytestingbelocal-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('meir-minzer-oshman-candistributeduniformitytestingbelocal-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{MMO19,\n  author    = {Uri Meir and\n               Dor Minzer and\n               Rotem Oshman},\n  title     = {Can Distributed Uniformity Testing Be Local?},\n  booktitle = {2019 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2019},\n  pages     = {228--237},\n  publisher = {{ACM}},\n  year      = {2019},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[MMO19]&lt;/span&gt; Considers a similar setting as [FMO18], but allowing $\\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\\ell$-bit Boolean function.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"diakonikolas-gouleakis-kane-rao-communicationandmemoryefficienttestingofdiscretedistributions-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Communication and Memory Efficient Testing of Discrete Distributions.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Ilias Diakonikolas;  Themis Gouleakis;  Daniel M. Kane;  and  Sankeerth Rao.\n</span>\n\n  \n\n</span>\n\n  In <i>32nd Conference on Learning Theory, COLT 2019</i>, volume 99, of <i>Proceedings of Machine Learning Research</i>, pages 1070–1106,  2019. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[DGKR19]</span> Considers global memory constraints, in the blackboard model: the communication bound is for the total communication over all users, and as such the results are incomparable to works on local constraints, though some of the techniques can carry over. Establish tight or near-tight bounds for identity testing of discrete distributions; the techniques also apply to testing under memory constraints.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/diakonikolas-gouleakis-kane-rao-communicationandmemoryefficienttestingofdiscretedistributions-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('diakonikolas-gouleakis-kane-rao-communicationandmemoryefficienttestingofdiscretedistributions-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{DGKR19,\n  title = \t {Communication and Memory Efficient Testing of Discrete Distributions},\n  author = \t {Diakonikolas, Ilias and Gouleakis, Themis and Kane, Daniel M. and Rao, Sankeerth},\n  booktitle = \t {32nd Conference on Learning Theory, {COLT} 2019},\n  pages = \t {1070--1106},\n  year = \t {2019},\n  volume = \t {99},\n  series = \t {Proceedings of Machine Learning Research},\n  publisher = \t {PMLR},\n  pdf = \t {http://proceedings.mlr.press/v99/diakonikolas19a/diakonikolas19a.pdf},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[DGKR19]&lt;/span&gt; Considers global memory constraints, in the blackboard model: the communication bound is for the total communication over all users, and as such the results are incomparable to works on local constraints, though some of the techniques can carry over. Establish tight or near-tight bounds for identity testing of discrete distributions; the techniques also apply to testing under memory constraints.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"barnes-han-zgr-fisherinformationfordistributedestimationunderablackboardcommunicationprotocol-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Fisher Information for Distributed Estimation under a Blackboard Communication Protocol.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Leighton P. Barnes;  Yanjun Han;  and  Ayfer Özgür.\n</span>\n\n  \n\n</span>\n\n  In <i>ISIT</i>, pages 2704–2708,  2019. IEEE\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[BHÖ19]</span> Provides general lower bounds for parameter estimation (and, in some cases, nonparametric density estimation) under $\\ell_2$ loss for interactive protocols (blackboard model) under communication constraints, and instantiate it to obtain tight bounds for various statistical models such as Gaussian, product Bernoulli, and discrete distribution estimation. At its core, the lower bounds rely on a Cramér–Rao/van Trees-type approach, which leaves the (trace of) the Fisher information matrix as quantity to analyze to get lower bounds.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/barnes-han-zgr-fisherinformationfordistributedestimationunderablackboardcommunicationprotocol-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('barnes-han-zgr-fisherinformationfordistributedestimationunderablackboardcommunicationprotocol-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{BHO19,\n  author    = {Leighton P. Barnes and\n               Yanjun Han and\n               Ayfer {\\&quot;{O}}zg{\\&quot;{u}}r},\n  title     = {Fisher Information for Distributed Estimation under a Blackboard Communication Protocol},\n  booktitle = {{ISIT}},\n  pages     = {2704--2708},\n  publisher = {{IEEE}},\n  year      = {2019},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[BHÖ19]&lt;/span&gt; Provides general lower bounds for parameter estimation (and, in some cases, nonparametric density estimation) under $\\ell_2$ loss for interactive protocols (blackboard model) under communication constraints, and instantiate it to obtain tight bounds for various statistical models such as Gaussian, product Bernoulli, and discrete distribution estimation. At its core, the lower bounds rely on a Cramér–Rao/van Trees-type approach, which leaves the (trace of) the Fisher information matrix as quantity to analyze to get lower bounds.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"duchi-rogers-lowerboundsforlocallyprivateestimationviacommunicationcomplexity-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Lower Bounds for Locally Private Estimation via Communication Complexity.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   John Duchi;  and  Ryan Rogers.\n</span>\n\n  \n\n</span>\n\n  In <i>32nd Conference on Learning Theory, COLT 2019</i>, volume 99, of <i>Proceedings of Machine Learning Research</i>, pages 1161–1191,  2019. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[DR19]</span> Develops a communication-complexity-based methodology for lower bounds under LDP constraints in the blackboard communication model. Obtains lower bounds for mean estimation of Bernoulli products under general $\\ell_p$ losses, as well as tight bounds for mean estimation of Gaussian and sparse Gaussian distributions under the $\\ell_2$ loss.</span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/duchi-rogers-lowerboundsforlocallyprivateestimationviacommunicationcomplexity-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('duchi-rogers-lowerboundsforlocallyprivateestimationviacommunicationcomplexity-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{DR19,\n  title = \t {Lower Bounds for Locally Private Estimation via Communication Complexity},\n  author = \t {Duchi, John and Rogers, Ryan},\n  booktitle = \t {32nd Conference on Learning Theory, {COLT} 2019},\n  pages = \t {1161--1191},\n  year = \t {2019},\n  volume = \t {99},\n  series = \t {Proceedings of Machine Learning Research},\n  publisher = \t {PMLR},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[DR19]&lt;/span&gt; Develops a communication-complexity-based methodology for lower bounds under LDP constraints in the blackboard communication model. Obtains lower bounds for mean estimation of Bernoulli products under general $\\ell_p$ losses, as well as tight bounds for mean estimation of Gaussian and sparse Gaussian distributions under the $\\ell_2$ loss.}\n }\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2018\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2018')\"\n      onkeypress=\"toggleGroup('group_2018')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2018</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"han-mukherjee-zgr-weissman-distributedstatisticalestimationofhighdimensionalandnonparametricdistributions-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Distributed Statistical Estimation of High-Dimensional and Non-parametric Distributions.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Yanjun Han;  Pritam Mukherjee;  Ayfer Özgür;  and  Tsachy Weissman.\n</span>\n\n  \n\n</span>\n\n  In <i>2018 IEEE International Symposium on Information Theory (ISIT'18)</i>, pages 506–510,  2018. \n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[HMÖW18]</span> Lower bounds on distributed estimation (in total variation distance) of several families of distributions under communication constraints. Results apply to noniteractive protocols (a gap in the argument prevents the extension to interactive).</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/han-mukherjee-zgr-weissman-distributedstatisticalestimationofhighdimensionalandnonparametricdistributions-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('han-mukherjee-zgr-weissman-distributedstatisticalestimationofhighdimensionalandnonparametricdistributions-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{HMOW-ISIT18,\n  author    = {Yanjun Han and Pritam Mukherjee and Ayfer {{\\&quot;O}zg{\\&quot;u}r} and Tsachy Weissman},\n  title = {Distributed Statistical Estimation of High-Dimensional and Non-parametric Distributions},\n  booktitle = {2018 IEEE International Symposium on Information Theory (ISIT&#x27;18)},\nyear = {2018},\npages={506--510},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[HMÖW18]&lt;/span&gt; Lower bounds on distributed estimation (in total variation distance) of several families of distributions under communication constraints. Results apply to noniteractive protocols (a gap in the argument prevents the extension to interactive).&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fischer-meir-oshman-distributeduniformitytesting-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Distributed Uniformity Testing.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Orr Fischer;  Uri Meir;  and  Rotem Oshman.\n</span>\n\n  \n\n</span>\n\n  In <i>2018 ACM Symposium on Principles of Distributed Computing, PODC 2018</i>, pages 455–464,  2018. ACM\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[FMO18]</span> Studies distributed uniformity testing in a setting where each user observe multiple samples, and communicates a single bit to the referee who is required to use a simple aggregation rule, e.g., AND or a threshold. The goal is then to minimize the number of samples required per user. Also contains results on uniformity testing in other distributed models, such as the CONGEST or LOCAL models.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fischer-meir-oshman-distributeduniformitytesting-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fischer-meir-oshman-distributeduniformitytesting-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{FMO18,\n  author    = {Orr Fischer and\n               Uri Meir and\n               Rotem Oshman},\n  title     = {Distributed Uniformity Testing},\n  booktitle = {2018 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2018},\n  pages     = {455--464},\n  publisher = {{ACM}},\n  year      = {2018},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[FMO18]&lt;/span&gt; Studies distributed uniformity testing in a setting where each user observe  multiple samples, and  communicates a single bit to the referee who  is  required  to  use a simple  aggregation rule, e.g., AND or a threshold. The goal is then to minimize the number of samples required per user. Also contains results on uniformity testing in other distributed models, such as the CONGEST or LOCAL models.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"han-zgr-weissman-geometriclowerboundsfordistributedparameterestimationundercommunicationconstraints-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Yanjun Han;  Ayfer Özgür;  and  Tsachy Weissman.\n</span>\n\n  \n\n</span>\n\n  In <i>31st Conference on Learning Theory, COLT 2018</i>, volume 75, of <i>Proceedings of Machine Learning Research</i>, pages 3163–3188,  2018. PMLR\n  <span class=\"note\">See updated version, ˘rlhttps://arxiv.org/abs/1802.08417v3 (2020).</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[HÖW18]</span> Lower bounds on distributed parameter estimation under the $\\ell_2$ loss of several families of distributions, including high-dimensional, under communication constraints. Results for the latest version, using techniques similar to those of [ACLST20,ACT20d], extend to the blackboard model and include $\\ell_p$ losses.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/han-zgr-weissman-geometriclowerboundsfordistributedparameterestimationundercommunicationconstraints-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('han-zgr-weissman-geometriclowerboundsfordistributedparameterestimationundercommunicationconstraints-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{HOW18,\n  author    = {Yanjun Han and\n               Ayfer {\\&quot;{O}}zg{\\&quot;{u}}r and\n               Tsachy Weissman},\n  title     = {Geometric Lower Bounds for Distributed Parameter Estimation under\n               Communication Constraints},\n  booktitle = {31st Conference on Learning Theory, {COLT} 2018},\n  series    = {Proceedings of Machine Learning Research},\n  volume    = {75},\n  pages     = {3163--3188},\n  publisher = {{PMLR}},\n  year      = {2018},\n  note = {See updated version, \\url{https://arxiv.org/abs/1802.08417v3} (2020).},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[HÖW18]&lt;/span&gt; Lower bounds on distributed parameter estimation under the $\\ell_2$ loss of several families of distributions, including high-dimensional, under communication constraints. Results for the latest version, using techniques similar to those of [ACLST20,ACT20d], extend to the blackboard model and include $\\ell_p$ losses.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"duchi-jordan-wainwright-minimaxoptimalproceduresforlocallyprivateestimation-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Minimax optimal procedures for locally private estimation.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   John C. Duchi;  Michael I. Jordan;  and  Martin J. Wainwright.\n</span>\n\n  \n\n</span>\n\n  <i>J. Amer. Statist. Assoc.</i>, 113(521): 182–201.  2018.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[DJW18]</span> Results and techniques similar to those of [DJW13].</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/duchi-jordan-wainwright-minimaxoptimalproceduresforlocallyprivateestimation-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('duchi-jordan-wainwright-minimaxoptimalproceduresforlocallyprivateestimation-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article {DJW17,\n    AUTHOR = {Duchi, John C. and Jordan, Michael I. and Wainwright, Martin\n              J.},\n     TITLE = {Minimax optimal procedures for locally private estimation},\n   JOURNAL = {J. Amer. Statist. Assoc.},\n  FJOURNAL = {Journal of the American Statistical Association},\n    VOLUME = {113},\n      YEAR = {2018},\n    NUMBER = {521},\n     PAGES = {182--201},\n      ISSN = {0162-1459},\n   MRCLASS = {62C20 (62B10 62D05 62G07 62J12)},\n  MRNUMBER = {3803452},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[DJW18]&lt;/span&gt; Results and techniques similar to those of [DJW13].&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2017\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2017')\"\n      onkeypress=\"toggleGroup('group_2017')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2017</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"feldman-ageneralcharacterizationofthestatisticalquerycomplexity-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://proceedings.mlr.press/v65/feldman17c.html\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'feldman-ageneralcharacterizationofthestatisticalquerycomplexity-2017', 'http://proceedings.mlr.press/v65/feldman17c.html', event);\">\n    A General Characterization of the Statistical Query Complexity.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Vitaly Feldman.\n</span>\n\n  \n\n</span>\n\n  In  Satyen Kale;  and  Ohad Shamir., editor(s), volume 65, of <i>Proceedings of Machine Learning Research</i>, pages 785–830, Amsterdam, Netherlands, 07–10 Jul 2017. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[Feldman17]</span> Provides a characterization of SQ learning in terms of new \"statistical dimension;\" to be seen in view of the poly-factor equivalence between SQ learning and LDP-constrained/memory-constrained learnin (e.g., [KLNRS11,BDD98]). Includes applications to memory-limited streaming and communication-limited learning.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://proceedings.mlr.press/v65/feldman17c.html\"\n     onclick=\"log_download('feldman-ageneralcharacterizationofthestatisticalquerycomplexity-2017', 'http://proceedings.mlr.press/v65/feldman17c.html', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A General Characterization of the Statistical Query Complexity [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/feldman-ageneralcharacterizationofthestatisticalquerycomplexity-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('feldman-ageneralcharacterizationofthestatisticalquerycomplexity-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{Feldman17,\n  title = \t {A General Characterization of the Statistical Query Complexity},\n  author = \t {Vitaly Feldman},\n  pages = \t {785--830},\n  year = \t {2017},\n  editor = \t {Satyen Kale and Ohad Shamir},\n  volume = \t {65},\n  series = \t {Proceedings of Machine Learning Research},\n  address = \t {Amsterdam, Netherlands},\n  month = \t {07--10 Jul},\n  publisher =    {PMLR},\n  pdf = \t {http://proceedings.mlr.press/v65/feldman17c/feldman17c.pdf},\n  url = \t {http://proceedings.mlr.press/v65/feldman17c.html},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[Feldman17]&lt;/span&gt; Provides a characterization of SQ learning in terms of new &quot;statistical dimension;&quot; to be seen in view of the poly-factor equivalence between SQ learning and LDP-constrained/memory-constrained learnin (e.g., [KLNRS11,BDD98]). Includes applications to memory-limited streaming and communication-limited learning.&lt;/div&gt;}\n}\n  \n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2016\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2016')\"\n      onkeypress=\"toggleGroup('group_2016')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2016</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"braverman-garg-ma-nguyen-woodruff-communicationlowerboundsforstatisticalestimationproblemsviaadistributeddataprocessinginequality-2016\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Communication lower bounds for statistical estimation problems via a distributed data processing inequality.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Mark Braverman;  Ankit Garg;  Tengyu Ma;  Huy L. Nguyen;  and  David P. Woodruff.\n</span>\n\n  \n\n</span>\n\n  In <i>Symposium on Theory of Computing Conference, STOC'16</i>, pages 1011–1020,  2016. ACM\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[BGMNW16]</span> Significantly generalizes [GMN14], extending the lower bounds to the blackboard model, and the upper bounds to the SMP model. Includes tight results for sparse mean estimation. The lower bounds are obtained via a combination of strong data processing inequalities (SDPI) and the \"cut-and-paste\" property of Hellinger distance.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/braverman-garg-ma-nguyen-woodruff-communicationlowerboundsforstatisticalestimationproblemsviaadistributeddataprocessinginequality-2016\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('braverman-garg-ma-nguyen-woodruff-communicationlowerboundsforstatisticalestimationproblemsviaadistributeddataprocessinginequality-2016')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{BGMNW16,\n  author    = {Mark Braverman and\n               Ankit Garg and\n               Tengyu Ma and\n               Huy L. Nguyen and\n               David P. Woodruff},\n  title     = {Communication lower bounds for statistical estimation problems via\n               a distributed data processing inequality},\n  booktitle = {Symposium on Theory of Computing Conference, {STOC&#x27;16}},\n  pages     = {1011--1020},\n  publisher = {{ACM}},\n  year      = {2016},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[BGMNW16]&lt;/span&gt; Significantly generalizes [GMN14], extending the lower bounds to the blackboard model, and the upper bounds to the SMP model. Includes tight results for sparse mean estimation. The lower bounds are obtained via a combination of strong data processing inequalities (SDPI) and the &quot;cut-and-paste&quot; property of Hellinger distance.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"steinhardt-valiant-wager-memorycommunicationandstatisticalqueries-2016\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://proceedings.mlr.press/v49/steinhardt16.html\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'steinhardt-valiant-wager-memorycommunicationandstatisticalqueries-2016', 'http://proceedings.mlr.press/v49/steinhardt16.html', event);\">\n    Memory, Communication, and Statistical Queries.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Jacob Steinhardt;  Gregory Valiant;  and  Stefan Wager.\n</span>\n\n  \n\n</span>\n\n  In  Vitaly Feldman;  Alexander Rakhlin;  and  Ohad Shamir., editor(s), volume 49, of <i>Proceedings of Machine Learning Research</i>, pages 1490–1516, Columbia University, New York, New York, USA, 23–26 Jun 2016. PMLR\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[SVW16]</span> Studies memory- and communication-constrained learning, and provides a general framework (based on statistical query (SQ) learning) to obtain lower bounds against those. Note that this allows to prove exponential separations for some problems (such as learning parities), but the reductions inherently lose polynomial factors.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://proceedings.mlr.press/v49/steinhardt16.html\"\n     onclick=\"log_download('steinhardt-valiant-wager-memorycommunicationandstatisticalqueries-2016', 'http://proceedings.mlr.press/v49/steinhardt16.html', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Memory, Communication, and Statistical Queries [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/steinhardt-valiant-wager-memorycommunicationandstatisticalqueries-2016\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('steinhardt-valiant-wager-memorycommunicationandstatisticalqueries-2016')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@InProceedings{SVW16,\n  title = \t {Memory, Communication, and Statistical Queries},\n  author = \t {Jacob Steinhardt and Gregory Valiant and Stefan Wager},\n  pages = \t {1490--1516},\n  year = \t {2016},\n  editor = \t {Vitaly Feldman and Alexander Rakhlin and Ohad Shamir},\n  volume = \t {49},\n  series = \t {Proceedings of Machine Learning Research},\n  address = \t {Columbia University, New York, New York, USA},\n  month = \t {23--26 Jun},\n  publisher =    {PMLR},\n  url = \t {http://proceedings.mlr.press/v49/steinhardt16.html},\n  bibbase_note = \t {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[SVW16]&lt;/span&gt; Studies memory- and communication-constrained learning, and provides a general framework (based on statistical query (SQ) learning) to obtain lower bounds against those. Note that this allows to prove exponential separations for some problems (such as learning parities), but the reductions inherently lose polynomial factors.&lt;/div&gt;}\n}\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2014\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2014')\"\n      onkeypress=\"toggleGroup('group_2014')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2014</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"shamir-fundamentallimitsofonlineanddistributedalgorithmsforstatisticallearningandestimation-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Fundamental limits of online and distributed algorithms for statistical learning and estimation.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Ohad Shamir.\n</span>\n\n  \n\n</span>\n\n  In <i>Advances in Neural Information Processing Systems 27, NeurIPS'14</i>, pages 163–171,  2014. \n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[Sha14]</span> Considers estimation tasks under various information constraints, such as memory or communication. Establishes results for sequentially interactive protocols for those problems by proving a lower bound on the \"hide-and-seek\" problem, that is, the mean estimation problem for high-dimensional product Bernoulli distributions with 1-sparse mean vectors.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/shamir-fundamentallimitsofonlineanddistributedalgorithmsforstatisticallearningandestimation-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('shamir-fundamentallimitsofonlineanddistributedalgorithmsforstatisticallearningandestimation-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{Shamir14,\n  title={Fundamental limits of online and distributed algorithms for statistical learning and estimation},\n  author={Shamir, Ohad},\n  booktitle= {Advances in Neural Information Processing Systems 27, {NeurIPS&#x27;14}},\n  pages={163--171},\n  year={2014},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[Sha14]&lt;/span&gt; Considers estimation tasks under various information constraints, such as memory or communication. Establishes results for sequentially interactive protocols for those problems by proving a lower bound on the &quot;hide-and-seek&quot; problem, that is, the mean estimation problem for high-dimensional product Bernoulli distributions with 1-sparse mean vectors.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"garg-ma-nguyen-oncommunicationcostofdistributedstatisticalestimationanddimensionality-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  On Communication Cost of Distributed Statistical Estimation and Dimensionality.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Ankit Garg;  Tengyu Ma;  and  Huy L. Nguyen.\n</span>\n\n  \n\n</span>\n\n  In <i>Advances in Neural Information Processing Systems 27, NeurIPS'14</i>, pages 2726–2734,  2014. \n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[GMN14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols for various settings, specifically Gaussian mean estimation under $\\ell_2$ loss. Also incudes matching upper bounds in the blackboard model, which can be generalized to $\\ell_p$ in the sequentially interactive model.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/garg-ma-nguyen-oncommunicationcostofdistributedstatisticalestimationanddimensionality-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('garg-ma-nguyen-oncommunicationcostofdistributedstatisticalestimationanddimensionality-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{GMN14,\n  author    = {Ankit Garg and\n               Tengyu Ma and\n               Huy L. Nguyen},\n  title     = {On Communication Cost of Distributed Statistical Estimation and Dimensionality},\n  booktitle = {Advances in Neural Information Processing Systems 27, {NeurIPS&#x27;14}},\n  pages     = {2726--2734},\n  year      = {2014},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[GMN14]&lt;/span&gt; Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols for various settings, specifically Gaussian mean estimation under $\\ell_2$ loss. Also incudes matching upper bounds in the blackboard model, which can be generalized to $\\ell_p$ in the sequentially interactive model.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2013\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2013')\"\n      onkeypress=\"toggleGroup('group_2013')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2013</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"zhang-duchi-jordan-wainwright-informationtheoreticlowerboundsfordistributedstatisticalestimationwithcommunicationconstraints-2013\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1405.0782\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'zhang-duchi-jordan-wainwright-informationtheoreticlowerboundsfordistributedstatisticalestimationwithcommunicationconstraints-2013', 'https://arxiv.org/abs/1405.0782', event);\">\n    Information-theoretic lower bounds for distributed statistical estimation with communication constraints.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Yuchen Zhang;  John Duchi;  Michael I. Jordan;  and  Martin J. Wainwright.\n</span>\n\n  \n\n</span>\n\n  In <i>Advances in Neural Information Processing Systems 26, NeurIPS'13</i>, pages 2328–2336,  2013. \n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[ZDJW13]</span> and <span class=\"bluecite\">[DJWZ14]</span> Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols under communication constraints under $\\ell_2$ loss for various estimation problems, including Gaussian and Bernoulli mean estimation. Also includes some results for interactive protocols.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1405.0782\"\n     onclick=\"log_download('zhang-duchi-jordan-wainwright-informationtheoreticlowerboundsfordistributedstatisticalestimationwithcommunicationconstraints-2013', 'https://arxiv.org/abs/1405.0782', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Information-theoretic lower bounds for distributed statistical estimation with communication constraints [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhang-duchi-jordan-wainwright-informationtheoreticlowerboundsfordistributedstatisticalestimationwithcommunicationconstraints-2013\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhang-duchi-jordan-wainwright-informationtheoreticlowerboundsfordistributedstatisticalestimationwithcommunicationconstraints-2013')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{ZDJW13,\n  title={Information-theoretic lower bounds for distributed statistical estimation with communication constraints},\n  author={Zhang, Yuchen and Duchi, John and Jordan, Michael I. and Wainwright, Martin J.},\n  booktitle= {Advances in Neural Information Processing Systems 26, {NeurIPS&#x27;13}},\n  pages={2328--2336},\n  year={2013},\n  url = {https://arxiv.org/abs/1405.0782},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[ZDJW13]&lt;/span&gt; and &lt;span class=&quot;bluecite&quot;&gt;[DJWZ14]&lt;/span&gt; Uses strong data processing inequalities (SDPI) to obtain lower bounds for simultaneous message passing (SMP) protocols  under communication constraints under $\\ell_2$ loss for various estimation problems, including Gaussian and Bernoulli mean estimation. Also includes some results for interactive protocols.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"duchi-jordan-wainwright-localprivacyandstatisticalminimaxrates-2013\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Local Privacy and Statistical Minimax Rates.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   John C. Duchi;  Michael I. Jordan;  and  Martin J. Wainwright.\n</span>\n\n  \n\n</span>\n\n  In <i>focs13</i>, pages 429–438,  2013. IEEE Computer Society\n  <span class=\"note\">Full version at ˘rlhttps://arxiv.org/abs/1302.3203.</span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[DJW13]</span> Lower bounds on parameter estimation for several families of distributions under LDP constraints, via strong data processing inequalities (SDPI) and a locally private version of Le Cam, Fano, and Assouad's lemmata. Results apply to the one-dimensional setting, and in high dimensions for noninteractive protocols.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/duchi-jordan-wainwright-localprivacyandstatisticalminimaxrates-2013\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('duchi-jordan-wainwright-localprivacyandstatisticalminimaxrates-2013')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{DJW13:FOCS,\n  author    = {John C. Duchi and\n               Michael I. Jordan and\n               Martin J. Wainwright},\n  title     = {Local Privacy and Statistical Minimax Rates},\n  booktitle = focs13,\n  pages     = {429--438},\n  publisher = {{IEEE} Computer Society},\n  year      = {2013},\n  note = {Full version at \\url{https://arxiv.org/abs/1302.3203}.},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[DJW13]&lt;/span&gt; Lower bounds on parameter estimation for several families of distributions under LDP constraints, via strong data processing inequalities (SDPI) and a locally private version of Le Cam, Fano, and Assouad&#x27;s lemmata. Results apply to the one-dimensional setting, and in high dimensions for noninteractive protocols.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2011\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2011')\"\n      onkeypress=\"toggleGroup('group_2011')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2011</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1137/090756090\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011', 'https://doi.org/10.1137/090756090', event);\">\n    What can we learn privately?.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Shiva Prasad Kasiviswanathan;  Homin K. Lee;  Kobbi Nissim;  Sofya Raskhodnikova;  and  Adam Smith.\n</span>\n\n  \n\n</span>\n\n  <i>SIAM J. Comput.</i>, 40(3): 793–826.  2011.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[KLNRS11]</span> Provides the first connection (and poly-factor equivalence) between learning under local privacy (LDP) constraints and statistical query (SQ) learning.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1137/090756090\"\n     onclick=\"log_download('kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011', 'https://doi.org/10.1137/090756090', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"What can we learn privately? [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1137/090756090\"\n     onclick=\"log_download('kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011', 'http://doi.org/10.1137/090756090', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('kasiviswanathan-lee-nissim-raskhodnikova-smith-whatcanwelearnprivately-2011')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{KLNRS11,\n    AUTHOR = {Kasiviswanathan, Shiva Prasad and Lee, Homin K. and Nissim,\n              Kobbi and Raskhodnikova, Sofya and Smith, Adam},\n     TITLE = {What can we learn privately?},\n   JOURNAL = {SIAM J. Comput.},\n  FJOURNAL = {SIAM Journal on Computing},\n    VOLUME = {40},\n      YEAR = {2011},\n    NUMBER = {3},\n     PAGES = {793--826},\n      ISSN = {0097-5397},\n   MRCLASS = {68Q32},\n  MRNUMBER = {2823508},\nMRREVIEWER = {Martin Anthony},\n       DOI = {10.1137/090756090},\n       URL = {https://doi.org/10.1137/090756090},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[KLNRS11]&lt;/span&gt; Provides the first connection (and poly-factor equivalence) between learning under local privacy (LDP) constraints and statistical query (SQ) learning.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1998\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1998')\"\n      onkeypress=\"toggleGroup('group_1998')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1998</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"bendavid-dichterman-learningwithrestrictedfocusofattention-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1006/jcss.1998.1569\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'bendavid-dichterman-learningwithrestrictedfocusofattention-1998', 'https://doi.org/10.1006/jcss.1998.1569', event);\">\n    Learning with restricted focus of attention.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Shai Ben-David;  and  Eli Dichterman.\n</span>\n\n  \n\n</span>\n\n  <i>J. Comput. System Sci.</i>, 56(3): 277–298.  1998.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[BDD98]</span> Provides the first connection (and poly-factor equivalence) between learning with communication constraints (wRFA: \"restricted focus of attention'') and statistical query (SQ) learning.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1006/jcss.1998.1569\"\n     onclick=\"log_download('bendavid-dichterman-learningwithrestrictedfocusofattention-1998', 'https://doi.org/10.1006/jcss.1998.1569', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Learning with restricted focus of attention [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1006/jcss.1998.1569\"\n     onclick=\"log_download('bendavid-dichterman-learningwithrestrictedfocusofattention-1998', 'http://doi.org/10.1006/jcss.1998.1569', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/bendavid-dichterman-learningwithrestrictedfocusofattention-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('bendavid-dichterman-learningwithrestrictedfocusofattention-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{BenDavidD98,\n    AUTHOR = {Ben-David, Shai and Dichterman, Eli},\n     TITLE = {Learning with restricted focus of attention},\n   JOURNAL = {J. Comput. System Sci.},\n  FJOURNAL = {Journal of Computer and System Sciences},\n    VOLUME = {56},\n      YEAR = {1998},\n    NUMBER = {3},\n     PAGES = {277--298},\n      ISSN = {0022-0000},\n   MRCLASS = {68Q32 (68T05)},\n  MRNUMBER = {1633977},\n       DOI = {10.1006/jcss.1998.1569},\n       URL = {https://doi.org/10.1006/jcss.1998.1569},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[BDD98]&lt;/span&gt; Provides the first connection (and poly-factor equivalence) between learning with communication constraints (wRFA: &quot;restricted focus of attention&#x27;&#x27;) and statistical query (SQ) learning.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1995\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1995')\"\n      onkeypress=\"toggleGroup('group_1995')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1995</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.2307/3318681\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995', 'https://doi.org/10.2307/3318681', event);\">\n    Applications of the Van Trees inequality: a Bayesian Cramér-Rao bound.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   Richard D. Gill;  and  Boris Y. Levit.\n</span>\n\n  \n\n</span>\n\n  <i>Bernoulli</i>, 1(1-2): 59–79.  1995.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[GL95]</span> Provides a good and self-contained primer and derivation of the van Trees inequality and its uses.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.2307/3318681\"\n     onclick=\"log_download('gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995', 'https://doi.org/10.2307/3318681', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Applications of the Van Trees inequality: a Bayesian Cramér-Rao bound [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.2307/3318681\"\n     onclick=\"log_download('gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995', 'http://doi.org/10.2307/3318681', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gill-levit-applicationsofthevantreesinequalityabayesiancramrraobound-1995')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GillR95,\n    AUTHOR = {Gill, Richard D. and Levit, Boris Y.},\n     TITLE = {Applications of the {V}an {T}rees inequality: a {B}ayesian\n              {C}ram\\&#x27;{e}r-{R}ao bound},\n   JOURNAL = {Bernoulli},\n  FJOURNAL = {Bernoulli. Official Journal of the Bernoulli Society for\n              Mathematical Statistics and Probability},\n    VOLUME = {1},\n      YEAR = {1995},\n    NUMBER = {1-2},\n     PAGES = {59--79},\n      ISSN = {1350-7265},\n   MRCLASS = {62F10},\n  MRNUMBER = {1354456},\nMRREVIEWER = {V. K. Rohatgi},\n       DOI = {10.2307/3318681},\n       URL = {https://doi.org/10.2307/3318681},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[GL95]&lt;/span&gt; Provides a good and self-contained primer and derivation of the van Trees inequality and its uses.&lt;/div&gt;} \n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1993\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1993')\"\n      onkeypress=\"toggleGroup('group_1993')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1993</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tsitsiklis-decentralizeddetection-1993\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Decentralized detection.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n   John N. Tsitsiklis.\n</span>\n\n  \n\n</span>\n\n  In  H. V. Poor;  and  J. B. Thomas., editor(s), <i>Advances in Statistical Signal Processing</i>, volume 2, pages 297–344,  1993. JAI Press\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><div class=\"well well-small bibbase\"><span class=\"bluecite\">[Tsi93]</span> Considers <em>simple</em> hypothesis testing in a distributed setting, under communication constraints, and shows that for this problem public-coin (noninteractive) protocols are no more powerful than private-coin protocols.</div></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tsitsiklis-decentralizeddetection-1993\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tsitsiklis-decentralizeddetection-1993')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{Tsitsiklis93,\n  title={Decentralized detection},\n  author={Tsitsiklis, John N.},\n  booktitle={Advances in Statistical Signal Processing},\n  year={1993},\n  volume = {2},\n  editor = {H. V. Poor and J. B. Thomas},\n  publisher = {JAI Press},\n  pages = {297--344},\n  bibbase_note = {&lt;div class=&quot;well well-small bibbase&quot;&gt;&lt;span class=&quot;bluecite&quot;&gt;[Tsi93]&lt;/span&gt; Considers &lt;em&gt;simple&lt;/em&gt; hypothesis testing in a distributed setting, under communication constraints, and shows that for this problem public-coin (noninteractive) protocols are no more powerful than private-coin protocols.&lt;/div&gt;}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);