Cooperative distributed Information Bottleneck

MATÍAS VERA; LEONARDO REY VEGA; PABLO PIANTANIDA

Aachen

Conferencia; IEEE International Symposium on Information Theory 2017; 2017

IEEE

This paper investigates a scenario where two distantnodes separately observe memoryless process, namelyX1 and X2, and can cooperate through multiple exchanges of messages withthe  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  arbitrarilydependent  on (X1,X2).  These  interactive  exchanges  yield  anexplicit  cooperation  that  helps  the  third  node  to  identify,  from the  distributed  observations X1 and X2,  useful  features  for  the inference 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.