Learning mixtures of spherical Gaussians: moment methods and spectral decompositions

TL;DR

This paper introduces a spectral method for efficiently estimating parameters of spherical Gaussian mixtures using low-order moments, achieving consistency without requiring component separation assumptions.

Contribution

It presents a novel spectral decomposition approach that provides consistent, computationally efficient estimation of mixture components under general position conditions.

Findings

Spectral decomposition yields consistent parameter estimates.

No minimum separation needed for estimation.

Method applies to mixtures with spherical covariances.

Abstract

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, without additional minimum separation assumptions needed by previous computationally efficient estimation procedures. Thus computational and information-theoretic barriers to efficient estimation in mixture models are precluded when the mixture components have means in general position and spherical covariances. Some connections are made to estimation problems related to independent component analysis.