TY - GEN

T1 - Fisher Information for Distributed Estimation under a Blackboard Communication Protocol

AU - Barnes, Leighton Pate

AU - Han, Yanjun

AU - Ozgur, Ayfer

N1 - Funding Information:
This work was supported in part by NSF award CCF-1704624 and by the Center for Science of Information (CSoI), an NSF Science and Technology Center, under grant agreement CCF- 0939370.
Publisher Copyright:
© 2019 IEEE.

PY - 2019/7

Y1 - 2019/7

N2 - We consider the problem of learning high-dimensional discrete distributions and structured (e.g. Gaussian) distributions in distributed networks, where each node in the network observes an independent sample from the underlying distribution and can use k bits to communicate its sample to a central processor. We consider a blackboard communication model, where nodes can share information interactively through a public blackboard but each node is restricted to write at most k bits on the final transcript. We characterize the impact of the communication constraint k on the minimax risk of estimating the underlying distribution under ℓ2 loss, and develop minimax lower bounds that apply in a unified way to many common statistical models. This is achieved by explicitly characterizing the Fisher information from the blackboard transcript.

AB - We consider the problem of learning high-dimensional discrete distributions and structured (e.g. Gaussian) distributions in distributed networks, where each node in the network observes an independent sample from the underlying distribution and can use k bits to communicate its sample to a central processor. We consider a blackboard communication model, where nodes can share information interactively through a public blackboard but each node is restricted to write at most k bits on the final transcript. We characterize the impact of the communication constraint k on the minimax risk of estimating the underlying distribution under ℓ2 loss, and develop minimax lower bounds that apply in a unified way to many common statistical models. This is achieved by explicitly characterizing the Fisher information from the blackboard transcript.

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U2 - 10.1109/ISIT.2019.8849821

DO - 10.1109/ISIT.2019.8849821

M3 - Conference contribution

AN - SCOPUS:85073172404

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2704

EP - 2708

BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019

Y2 - 7 July 2019 through 12 July 2019

ER -