|| The Double-Sided Information-Bottleneck Function
||Michael Dikshtein, Technion – Israel Institute of Technology, Israel; Or Ordentlich, Hebrew University of Jerusalem, Israel; Shlomo Shamai (Shitz), Technion – Israel Institute of Technology, Israel|
||D6-S1-T2: Information Bottleneck II
||Monday, 19 July, 22:00 - 22:20
||Monday, 19 July, 22:20 - 22:40
We consider a two-terminal variant (double-sided) of the information bottleneck problem, which is related to biclustering. In our setup, X and Y are dependent random variables and the problem is to find two independent channels P_U|X and P_V|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 correlation. We conjecture that Z and S channels are optimal when the correlation is 1 (i.e., X = Y), and provide supporting numerical evidence.