Support Vector Method for Multivariate Density Estimation

A new method for multivariate density estimation is developed based on the Support Vector Method (SVM) solution of inverse ill-posed problems. The solution has the form of a mixture of densities. This method with Gaussian kernels compared favorably to both Parzen's method and the Gaussian Mixture Model method. For synthetic data we achieve more accurate estimates for densities of 2, 6, 12, and 40 dimensions. 1 Introduction The problem of multivariate density estimation is important for many applications, in particular, for speech recognition [1] [7]. When the unknown density belongs to a parametric set satisfying certain conditions one can estimate it using the maximum likelihood (ML) method. Often these conditions are too restrictive. Therefore, non-parametric methods were proposed. The most popular of these, Parzen's method [5], uses the following estimate given data x 1 ; :::; x ` : P (t; fl ` ) = 1 ` ` X i=1 K fl ` (t \\Gamma x i ); (1) where K fl ` (t \\Gamma x i ) is a smoot...