# Factorized Mutual Information Maximization

## TL;DR

This paper explores the optimization of multi-information and mutual information across variable sets, proposing computationally efficient proxies and characterizing their maximizers to improve information-theoretic analysis.

## Contribution

It introduces a novel framework for maximizing multi-information using factorized mutual information proxies and characterizes their maximizers relative to traditional measures.

## Key findings

- Maximizers of the proposed functionals are characterized.
- Proxies reduce computational complexity in mutual information estimation.
- Relations between maximizers of proxies and original information measures are established.

## Abstract

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual information of two subsets of variables, at a lower computation and estimation complexity. We describe the maximizers and their relations to the maximizers of the multi-information and the mutual information.