Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints. Han, Y., Özgür, A., & Weissman, T. In Proceedings of the 31st Conference on Learning Theory, COLT 2018, volume 75, of Proceedings of Machine Learning Research, pages 3163–3188, 2018. PMLR. The arXiv (v3) version from 2020 corrects some issues and includes more results.
bibtex   
@inproceedings{HanOW18,
  author =        {Yanjun Han and Ayfer {\"{O}}zg{\"{u}}r and
                   Tsachy Weissman},
  booktitle =     {Proceedings of the 31st Conference on Learning
                   Theory, {COLT} 2018},
  pages =         {3163--3188},
  publisher =     {{PMLR}},
  series =        {Proceedings of Machine Learning Research},
  title =         {Geometric Lower Bounds for Distributed Parameter
                   Estimation under Communication Constraints},
  volume =        {75},
  year =          {2018},
  note = {The arXiv (v3) version from 2020 corrects some issues and includes more results.}
}

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