Discriminative Estimation of f-Divergence

We propose an approach for estimating f-divergences that exploits a new representa-tion of an f-divergence as a weighted integral of cost-weighted Bayes risks. We are there-fore able to reduce f-divergence estimation to a problem of a posterior conditional probabil-ity estimation. We provide both batch and online implementation of our approach and analyze their convergence. Empirically, we show our implementation compares favorably to other f-divergence estimators and demon-strate its application to an EEG dataset.