Relevant sparse codes with variational information bottleneck

In many applications, it is desirable to extract only the relevant aspects of data. A principled way to do this is the information bottleneck (IB) method, where one seeks a code that maximizes information about a 'relevance' variable, Y, while constraining the information encoded about the original data, X. Unfortunately however, the IB method is computationally demanding when data are high-dimensional and/or non-gaussian. Here we propose an approximate variational scheme for maximizing a lower bound on the IB objective, analogous to variational EM. Using this method, we derive an IB algorithm to recover features that are both relevant and sparse. Finally, we demonstrate how kernelized versions of the algorithm can be used to address a broad range of problems with non-linear relation between X and Y.

Estimating mutual information and multi--information in large networks

We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained with manageable computational effort. The same methods allow estimation of higher order, multi--information terms. These ideas are illustrated by analyses of gene expression, financial markets, and consumer preferences. In each case, information theoretic measures correlate with independent, intuitive measures of the underlying structures in the system.