Gaussian Mixture Estimation from Weighted Samples

TL;DR

This paper introduces a new EM-based method for accurately estimating Gaussian mixture parameters from weighted samples, addressing weight misinterpretation issues in existing methods, and demonstrating efficiency across dimensions.

Contribution

It presents a novel EM algorithm that correctly incorporates sample weights for Gaussian mixture estimation, improving accuracy over existing methods.

Findings

The proposed method accurately estimates parameters with weighted samples.

Existing methods often misinterpret weights, leading to incorrect estimates.

The approach is computationally efficient in any number of dimensions.

Abstract

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac mixture density over a continuous domain with weighted components. Hence, Gaussian mixture fitting is viewed as density re-approximation. In order to speed up computation, an expectation-maximization method is proposed that properly considers not only the sample locations, but also the corresponding weights. It is shown that methods from literature do not treat the weights correctly, resulting in wrong estimates. This is demonstrated with simple counterexamples. The proposed method works in any number of dimensions with the same computational load as standard Gaussian mixture estimators for unweighted samples.