  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.
