The Double-Sided Information Bottleneck Function

A double-sided variant of the information bottleneck method is considered. Let (X, Y) be a bivariate source characterized by a joint pmf P-XY. The problem is to find two independent channels P-U vertical bar X and P-V vertical bar 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.

Automated summary

The paper investigates a double-sided variant of the information bottleneck method, finding optimal channels in various scenarios and proposing an alternating maximization algorithm. This problem is closely related to biclustering.