(f,l)-divergences
Dario Garcia (NICTA)
NICTA SML SEMINARDATE: 2011-05-19
TIME: 11:00:00 - 12:00:00
LOCATION: NICTA - 7 London Circuit
CONTACT: JavaScript must be enabled to display this email address.
ABSTRACT:
f or Csiszar's divergences form a well-known family of divergence functionals for probability distributions, with many appealing properties. One of these properties is that they admit an integral representation in terms of statistical informations under the 0-1 loss for different prior probabilities (and so are closely related to Bayes risks). Based on this representation, we investigate the effect of substituting the 0-1 loss by another arbitrary loss function, yielding (f,l)-divergences. This new family is strictly larger than the original set of f-divergences, while sharing many of their nice properties if l appropriately chosen. More importantly, they provide alternative definitions of standard f-divergences in terms of surrogate risks. As a practical application of this theory, we construct a new order statistics based estimator for the Kullback-Leibler divergence, as well as a new bound in terms of Mahalanobis distances. We show that the estimator is competitive with the state of the art and apply it to several set-of-vectors clustering tasks.
This is joint work with Ulrike von Luxburg (MPI / UniversitAt Hamburg)
