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Feature selection, in the context of machine learning, is the process ofseparating the highly predictive feature from those that might be irrelevant orredundant. Information theory has been recognized as a useful concept for thistask, as the prediction power stems from the correlation, i.e., the mutualinformation, between features and labels. Many algorithms for feature selectionin the literature have adopted the Shannon-entropy-based mutual information. Inthis paper, we explore the possibility of using R\'enyi min-entropy instead. Inparticular, we propose an algorithm based on a notion of conditional R\'enyimin-entropy that has been recently adopted in the field of security andprivacy, and which is strictly related to the Bayes error. We prove that ingeneral the two approaches are incomparable, in the sense that we show that wecan construct datasets on which the R\'enyi-based algorithm performs betterthan the corresponding Shannon-based one, and datasets on which the situationis reversed. In practice, however, when considering datasets of real data, itseems that the R\'enyi-based algorithm tends to outperform the other one. Wehave effectuate several experiments on the BASEHOCK, SEMEION, and GISETTEdatasets, and in all of them we have indeed observed that the R\'enyi-basedalgorithm gives better results.

Feature selection in machine learning: R\'enyi min-entropy vs Shannon entropy