Learning mixtures of separated nonspherical Gaussians

Learning Mixtures of Separated non-Spherical Gaussians

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a local-search heuristic from Dempster, Laird and Rubin (1977). These do not provably run in polynomial time. We present the first algorithm that provably learns the co...

Learning Mixtures of Gaussians

Mixtures of Gaussians are among the most fundamental and widely used statistical models. Current techniques for learning such mixtures from data are local search heuristics with weak performance guarantees. We present the first provably correct algorithm for learning a mixture of Gaussians. This algorithm is very simple and returns the true centers of the Gaussians to within the precision speci...

Efficiently Learning Mixtures of Two Arbitrary Gaussians

Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We provide a polynomial-time algorithm for this problem for the case of two Gaussians in n dimensions (even if they overlap), with provably minimal assumptions on the Gaussians, and polynomial data requirements. In statistical terms, our estimator converges at an inverse ...

LEARNING MIXTURES OF GAUSSIANS Part I: Theory

Provably Learning Mixtures of Gaussians and More

Given a random sample, how can one accurately estimate the parameters of the probabilistic model that generated the data? This is a fundamental question in statistical inference and, more recently, in machine learning. One of the most widely studied instances of this problem is estimating the parameters of a mixture of Gaussians, since doing so is of fundamental importance in a wide range of su...