  Feature selection problems arise in a variety of applications, such as
microarray analysis, clinical prediction, text categorization, image
classification and face recognition, multi-label learning, and classification
of internet traffic. Among the various classes of methods, forward feature
selection methods based on mutual information have become very popular and are
widely used in practice. However, comparative evaluations of these methods have
been limited by being based on specific datasets and classifiers. In this
paper, we develop a theoretical framework that allows evaluating the methods
based on their theoretical properties. Our framework is grounded on the
properties of the target objective function that the methods try to
approximate, and on a novel categorization of features, according to their
contribution to the explanation of the class; we derive upper and lower bounds
for the target objective function and relate these bounds with the feature
types. Then, we characterize the types of approximations taken by the methods,
and analyze how these approximations cope with the good properties of the
target objective function. Additionally, we develop a distributional setting
designed to illustrate the various deficiencies of the methods, and provide
several examples of wrong feature selections. Based on our work, we identify
clearly the methods that should be avoided, and the methods that currently have
the best performance.
