CEO problem for belief sharing

2015 IEEE Information Theory Workshop (ITW) Pub Date : 2015-06-25 DOI:10.1109/ITW.2015.7133076

Aditya Vempaty, L. Varshney

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Abstract

We consider the CEO problem for belief sharing. Multiple subordinates observe independently corrupted versions of uniformly distributed data and transmit coded versions over rate-limited links to a CEO who then estimates the underlying data. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm's CEO estimating uniformly distributed beliefs about a sequence of events, before acting on them. Agents' observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents L and the sum rate R tend to infinity. We establish a 1/R2 convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the 1/R behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan-Zakai-Ziv bound.

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CEO分享信念的问题

我们考虑CEO问题的信念共享。多个下属独立地观察均匀分布数据的损坏版本，并通过速率限制的链接将编码版本传输给CEO，然后由后者估计底层数据。特工们在传送他们的观察结果之前是不允许开会的。这个公式是由一个公司的CEO在对一系列事件采取行动之前估计均匀分布信念的实际问题所激发的。通过给定的条件概率密度函数，将智能体的观测数据与底层数据联合分布。研究了当代理数L和和速率R趋于无穷时，在极限情况下，均方误差畸变的最小可达性的渐近行为。我们建立了失真的1/R2收敛性，这是离散CEO问题中的指数行为[Berger, Zhang, and Viswanathan(1996)]和高斯CEO问题中的1/R行为之间的一个中间机制[Viswanathan and Berger(1997)]。通过采用标量量化、分布式熵编码和中程估计的分层体系结构证明了其可实现性。利用贝叶斯Chazan-Zakai-Ziv界证明了其逆命题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2015 IEEE Information Theory Workshop (ITW)

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