Efficient global maximum likelihood estimation through kernel methods

Abstract

A new efficient technique for estimating probability densities from data through the application of the approximate global maximum likelihood (AGML) approach is proposed. It employs a composition of kernel functions to estimate the correct behavior of parameters involved in the expression of the unknown probability density. Convergence to the optimal solution is guaranteed by a deterministic learning framework when low discrepancy sequences are used to generate the centers of the kernels. Trials on mixture of Gaussians show that the proposed semi-local technique is able to efficiently approximate the maximum likelihood solution even in complex situations where implementations based on standard neural networks require an excessive computational cost.