Correcting the Kullback-Leibler distance for feature selection

A frequent practice in feature selection is to maximize the Kullback-Leibler (K-L) distance between target classes. In this note we show that this common custom is frequently suboptimal, since it fails to take into account the fact that classification occurs using a finite number of samples. In classification, the variance and higher order moments of the likelihood function should be taken into account to select feature subsets, and the Kullback Leibler distance only relates to the mean separation. We derive appropriate expressions and show that these can lead to major increases in performance.