Risk-Based Generalizations of f-divergences

García-García, D.; von Luxburg, U.; Santos-Rodríguez, R.

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Risk-Based Generalizations of f-divergences

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von Luxburg, U.
Research Group Machines Learning Theory, Max Planck Institute for Intelligent Systems, Max Planck Society;

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García-García, D., von Luxburg, U., & Santos-Rodríguez, R. (2011). Risk-Based Generalizations of f-divergences. In 28th International Conference on Machine Learning (ICML 2011) (pp. 417-424).

Cite as: https://hdl.handle.net/11858/00-001M-0000-0010-4CAB-9

Abstract

We derive a generalized notion of f-divergences, called (f,l)-divergences. We show that this generalization enjoys many of the nice properties of f-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.