Communication lower bounds for statistical estimation problems via a distributed data processing inequality. Braverman, M., Garg, A., Ma, T., Nguyen, H. L., & Woodruff, D. P. In Symposium on Theory of Computing Conference, STOC'16, pages 1011–1020, 2016. ACM.
[BGMNW16] 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.

bibtex   
@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>}
}

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