Theoretical Foundations of Forward Feature Selection Methods based on Mutual Information

TL;DR

This paper develops a theoretical framework to evaluate forward feature selection methods based on mutual information, analyzing their properties, limitations, and providing guidance on their effectiveness and pitfalls.

Contribution

It introduces a theoretical evaluation framework for mutual information-based feature selection, including bounds, feature categorization, and analysis of method deficiencies.

Findings

Identifies which methods to avoid based on theoretical analysis.

Provides bounds and feature categorization for better understanding of methods.

Illustrates deficiencies with examples and distributional settings.

Abstract

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.