About Filter Criteria for Feature Selection in Regression

Selecting the best group of features from high-dimensional datasets is an important challenge in machine learning. Indeed problems with hundreds of features have now become usual. In the context of filter methods, the selected relevance criterion used for filtering is the key factor of a feature selection method. To select an appropriate criterion among the numerous existing ones, this paper proposes a list of six necessary properties. This paper describes then three relevance criteria, the mutual information, the noise variance and the adjusted R-squared, and compares them in the view of the aforementioned properties. Any new, or popular, criterion could be analysed in the light of these properties.