Tensor decomposition for learning Gaussian mixtures from moments

TL;DR

This paper introduces a tensor decomposition approach for accurately recovering Gaussian mixture models from data moments, demonstrating its effectiveness through theoretical guarantees and empirical experiments.

Contribution

It presents a novel tensor decomposition method for Gaussian mixture recovery with proven identifiability and a simple linear algebra algorithm, outperforming existing methods.

Findings

Tensor decomposition can uniquely identify Gaussian mixtures.

The proposed algorithm is simple and effective.

Experimental results show improved recovery accuracy.

Abstract

In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric tensor decomposition methods for tackling this problem, where the tensor is built from empirical moments of the data distribution. We consider identifiable tensors, which have a unique decomposition, showing that moment tensors built from spherical Gaussian mixtures have this property. We prove that symmetric tensors with interpolation degree strictly less than half their order are identifiable and we present an algorithm, based on simple linear algebra operations, to compute their decomposition. Illustrative experimentations show the impact of the tensor decomposition method for recovering Gaussian mixtures, in comparison with other state-of-the-art approaches.