Risk-based generalizations of f-divergences

We derive a generalized notion of f-divergences, called (f,l)-divergences. We show that this generalization enjoys many of the nice properties of/-divergences, although it is a richer family. It also provides alternative definitions of standard divergences in terms of surrogate risks. As a first practical application of this theory, we derive a new estimator for the Kulback-Leibler divergence that we use for clustering sets of vectors