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Discriminative Estimation of f-Divergence

We propose an approach for estimating f divergences that exploits a new representation of an f -divergence as a weighted integral of cost-weighted Bayes risks. We are therefore able to reduce f -divergence estimation to a problem of a posterior conditional probability 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 demonstrate its application to an EEG dataset.