Distribution of Mutual Information from Complete and Incomplete Data
Abstract
Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sampletopopulation inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a secondorder Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(1/n^3), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes the distribution of mutual information become a concrete alternative to descriptive mutual information in many applications which would benefit from moving to the inductive side. Some of these prospective applications are discussed, and one of them, namely feature selection, is shown to perform significantly better when inductive mutual information is used.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:cs/0403025
 Bibcode:
 2004cs........3025H
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Artificial Intelligence;
 Computer Science  Information Theory;
 Mathematics  Statistics;
 I.2
 EPrint:
 26 pages, LaTeX, 5 figures, 4 tables