Theoretical evaluation of feature selection methods based on mutual information

Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that allows obtaining the true feature ordering of two-dimensional sequential forward feature selection methods based on mutual information, which is independent of entropy or mutual information estimation methods, classifiers, or datasets, and leads to an undoubtful comparison of the methods. Moreover, the theoretical framework unveils problems intrinsic to some methods that are otherwise difficult to detect, namely inconsistencies in the construction of the objective function used to select the candidate features, due to various types of indeterminations and to the possibility of the entropy of continuous random variables taking null and negative values.