Gaussianization: An Efficient Multivariate Density Estimation Technique for Statistical Signal Processing

Authors:
Deniz Erdogmus;Robert Jenssen;Yadunandana N. Rao;Jose C. Principe
Affiliations:
CSEE Department, Oregon Health and Science University, Portland, USA;Department of Physics, University of Tromso, Tromso, Norway;Motorola Corporation, Plantation, USA;CNEL, ECE Department, University of Florida, Gainesville, USA
Venue:
Journal of VLSI Signal Processing Systems
Year:
2006

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Abstract

Multivariate density estimation is an important problem that is frequently encountered in statistical learning and signal processing. One of the most popular techniques is Parzen windowing, also referred to as kernel density estimation. Gaussianization is a procedure that allows one to estimate multivariate densities efficiently from the marginal densities of the individual random variables. In this paper, we present an optimal density estimation scheme that combines the desirable properties of Parzen windowing and Gaussianization, using minimum Kullback---Leibler divergence as the optimality criterion for selecting the kernel size in the Parzen windowing step. The utility of the estimate is illustrated in classifier design, independent components analysis, and Prices' theorem.