The multi-layer information bottleneck problem

Qianqian Yang (1) , Pablo Piantanida (2) , Deniz Gunduz (1)

1 Imperial College London
2 L2S - Laboratoire des signaux et systèmes

The muti-layer information bottleneck (IB) problem, where information is propagated (or successively refined) from layer to layer, is considered. Based on information forwarded by the preceding layer, each stage of the network is required to preserve a certain level of relevance with regards to a specific hidden variable, quantified by the mutual information. The hidden variables and the source can be arbitrarily correlated. The optimal trade-off between rates of relevance and compression (or complexity) is obtained through a singleletter characterization, referred to as the rate-relevance region. Conditions of successive refinabilty are given. Binary source with BSC hidden variables and binary source with BSC/BEC mixed hidden variables are both proved to be successively refinable. We further extend our result to Guassian models. A counterexample of successive refinability is also provided.

Domaines: Théorie de l'information [cs.IT]; Réseaux et télécommunications [cs.NI]; Théorie de l'information et codage [math.IT]; Statistiques [math.ST]

Qianqian Yang, Pablo Piantanida, Deniz Gunduz. The multi-layer information bottleneck problem. 2017 IEEE Information Theory Workshop (ITW), Nov 2017, Kaohsiung, France. pp.404-408, ⟨10.1109/ITW.2017.8278006⟩. ⟨hal-01742326⟩