The Double-Sided Information Bottleneck Function

• Published in: Entropy (Basel, Switzerland) Vol. 24; no. 9; p. 1321
• Main Authors: Dikshtein, Michael, Ordentlich, Or, Shamai (Shitz), Shlomo
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2022; MDPI
• Subjects: Algorithms; biclustering; Bivariate analysis; Channels; Clustering; Codes; Correlation; Data compression; Gene expression; Hypothesis testing; information bottleneck; Information sources; lossy compression; Optimization; Pattern recognition; Random variables; remote source coding
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e24091321

A double-sided variant of the information bottleneck method is considered. Let (X,Y) be a bivariate source characterized by a joint pmf PXY. The problem is to find two independent channels PU|X and PV|Y (setting the Markovian structure U→X→Y→V), that maximize I(U;V) subject to constraints on the relevant mutual information expressions: I(U;X) and I(V;Y). For jointly Gaussian X and Y, we show that Gaussian channels are optimal in the low-SNR regime but not for general SNR. Similarly, it is shown that for a doubly symmetric binary source, binary symmetric channels are optimal when the correlation is low and are suboptimal for high correlations. We conjecture that Z and S channels are optimal when the correlation is 1 (i.e., X=Y) and provide supporting numerical evidence. Furthermore, we present a Blahut–Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering.