Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints. Han, Y., Özgür, A., & Weissman, T. In 31st Conference on Learning Theory, COLT 2018, volume 75, of Proceedings of Machine Learning Research, pages 3163–3188, 2018. PMLR. See updated version, ˘rlhttps://arxiv.org/abs/1802.08417v3 (2020).
[HÖW18] 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.

bibtex   
@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>}
}

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