Distributed Cooperative Information Bottleneck

MATÍAS ALEJANDRO VERA; LEONARDO REY VEGA; PABLO PIANTANIDA

Aachen

Simposio; IEEE International Symposium on Information Theory (ISIT); 2017

This paper investigates a scenario where two distantnodes separately observe memoryless process, namely X1 and X2 ,and can cooperate through multiple exchanges of messages withthe goal of enabling a third node to learn ?relevant informa-tion? (measured in terms of a multi-letter mutual information)about some hidden memoryless process Y, which is arbitrarilydependent on (X1, X2). These interactive exchanges yield anexplicit cooperation that helps the third node to identify, fromthe distributed observations X1 and X2 , useful features for theinference of Y. An inner and an outer bound to the rate-relevanceregion of this problem is derived. Optimal characterization ofthe rate-relevance region under two different conditions on thedependence structures of the involved variables is showed. Also,two examples for Gaussian sources are studied.