Robust Feature Selection by Mutual Information Distributions

TL;DR

This paper develops a Bayesian approach to analyze the distribution of mutual information for feature selection, providing analytical expressions and asymptotic approximations, and demonstrates improved performance in incremental learning tasks.

Contribution

It introduces a Bayesian distribution-based method for mutual information, with analytical formulas and asymptotic approximations, enhancing feature selection in incremental learning.

Findings

The Bayesian approach outperforms traditional empirical mutual information methods.

Analytical expressions for mean and variance of mutual information are derived.

The method efficiently handles incomplete samples in feature selection.

Abstract

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must consider sample-to-population inferential approaches. This paper deals with the distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean and an analytical approximation of the variance are reported. Asymptotic approximations of the distribution are proposed. The results are applied to the problem of selecting features for incremental learning and classification of the naive Bayes classifier. A fast, newly defined method is shown to outperform the traditional approach based on empirical mutual information on a number of real data sets. Finally, a theoretical development is reported that allows one to efficiently extend the above methods to incomplete samples in an easy and effective way.