On Communication Cost of Distributed Statistical Estimation and Dimensionality. Garg, A., Ma, T., & Nguyen, H. L. In *Advances in Neural Information Processing Systems 27, NeurIPS'14*, pages 2726–2734, 2014. [GMN14] 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.

bibtex @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>}
}

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