Learning Diagonal Gaussian Mixture Models and Incomplete Tensor Decompositions

TL;DR

This paper introduces a method using generating polynomials for learning parameters in diagonal Gaussian mixture models by computing incomplete symmetric tensor decompositions, with stability analysis and numerical validation.

Contribution

It presents a novel approach combining generating polynomials and tensor decomposition techniques to learn Gaussian mixture models more accurately and efficiently.

Findings

Parameters are highly accurate when moments are precise.

The tensor approximation method effectively learns Gaussian mixture models.

Numerical experiments validate the approach.

Abstract

This paper studies how to learn parameters in diagonal Gaussian mixture models. The problem can be formulated as computing incomplete symmetric tensor decompositions. We use generating polynomials to compute incomplete symmetric tensor decompositions and approximations. Then the tensor approximation method is used to learn diagonal Gaussian mixture models. We also do the stability analysis. When the first and third order moments are sufficiently accurate, we show that the obtained parameters for the Gaussian mixture models are also highly accurate. Numerical experiments are also provided.