Density estimation with minimization of U-divergence

Authors:
Kanta Naito;Shinto Eguchi
Affiliations:
Department of Mathematics, Shimane University, Matsue, Japan 690-8504;The Institute of Statistical Mathematics, Tokyo, Japan 190-8562
Venue:
Machine Learning
Year:
2013

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Abstract

This paper is concerned with density estimation based on the stagewise minimization of the U-divergence. The U-divergence is a general divergence measure involving a convex function U which includes the Kullback-Leibler divergence and the L 2 norm as special cases. The algorithm to yield the density estimator is closely related to the boosting algorithm and it is shown that the usual kernel density estimator can also be seen as a special case of the proposed estimator. Non-asymptotic error bounds of the proposed estimators are developed and numerical experiments show that the proposed estimators often perform better than several existing methods for density estimation.