Robust Feature Selection by Mutual Information Distributions

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.

8 two-column pages

References in corpus (1)

• An evaluation of Naive Bayesian anti-spam filtering

Cited by in corpus (4)

• Bootstrap Methods for the Empirical Study of Decision-Making and Information Flows in Social Systems
• Bayesian Treatment of Incomplete Discrete Data applied to Mutual Information and Feature Selection
• A Novel Weighted Combination Method for Feature Selection using Fuzzy Sets
• Distribution of Mutual Information from Complete and Incomplete Data