Variational Information Maximization for Feature Selection

TL;DR

This paper introduces a new variational information maximization framework for feature selection that overcomes limitations of existing methods by providing more accurate mutual information bounds, leading to improved feature selection performance.

Contribution

It proposes a flexible variational approach to approximate mutual information, offering a novel framework that outperforms existing information-theoretic feature selection methods.

Findings

The proposed method significantly outperforms existing approaches.

The framework is proven optimal under tree graphical models.

Experiments validate the effectiveness of the new approach.

Abstract

Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class labels. Practical methods are forced to rely on approximations due to the difficulty of estimating mutual information. We demonstrate that approximations made by existing methods are based on unrealistic assumptions. We formulate a more flexible and general class of assumptions based on variational distributions and use them to tractably generate lower bounds for mutual information. These bounds define a novel information-theoretic framework for feature selection, which we prove to be optimal under tree graphical models with proper choice of variational distributions. Our experiments demonstrate that the proposed method strongly outperforms existing information-theoretic feature selection approaches.