PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Kullback-Leibler Divergence Estimation of Continuous Distributions
Fernando Perez-Cruz
In: IEEE International Symposium on Information Theory (ISIT), July 2008, Toronto, Canada.

Abstract

We present a method for estimating the KL divergence between continuous densities and we prove it converges almost surely. Divergence estimation is typically solved estimating the densities first. Our main result shows this intermediate step is unnecessary and that the divergence can be either estimated using the empirical cdf or k-nearest-neighbour density estimation, which does not converge to the true measure for finite k. The convergence proof is based on describing the statistics of our estimator using waiting-times distributions, as the exponential or Erlang. We illustrate the proposed estimators and show how they compare to existing methods based on density estimation, and we also outline how our divergence estimators can be used for solving the two-sample problem.

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EPrint Type:Conference or Workshop Item (Talk)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4910
Deposited By:Fernando Perez-Cruz
Deposited On:24 March 2009