Distributed cooperative information bottleneck

Matias Vera (1) , Leonardo Rey Vega (1) , Pablo Piantanida (2)

1 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
2 L2S - Laboratoire des signaux et systèmes

This paper investigates a scenario where two distant nodes separately observe memoryless process, namely X 1 and X 2 , and can cooperate through multiple exchanges of messages with the goal of enabling a third node to learn “relevant information” (measured in terms of a multi-letter mutual information) about some hidden memoryless process Y, which is arbitrarily dependent on (X 1 , X 2 ). These interactive exchanges yield an explicit cooperation that helps the third node to identify, from the distributed observations X 1 and X 2 , useful features for the inference of Y. An inner and an outer bound to the rate-relevance region of this problem is derived. Optimal characterization of the rate-relevance region under two different conditions on the dependence structures of the involved variables is showed. Also, two examples for Gaussian sources are studied.

Domains: Information Theory [cs.IT]; Networking and Internet Architecture [cs.NI]; Information Theory [math.IT]; Statistics [math.ST]

Matias Vera, Leonardo Rey Vega, Pablo Piantanida. Distributed cooperative information bottleneck. 2017 IEEE International Symposium on Information Theory (ISIT), Jun 2017, Aachen, Germany. ⟨10.1109/ISIT.2017.8006620⟩. ⟨hal-01742331⟩