Local Minima Structures in Gaussian Mixture Models

arXiv:2009.13040v3 Announce Type: replace-cross
Abstract: We investigate the landscape of the negative log-likelihood function of Gaussian Mixture Models (GMMs) with a general number of components in the population limit. As the objective function is non-convex, there can be multiple local minima that are not globally optimal, even for well-separated mixture models. Our study reveals that all local minima share a common structure that partially identifies the cluster centers (i.e., means of the Gaussian components) of the true location mixture. Specifically, …

abstract arxiv components cs.lg function general landscape likelihood math.st multiple negative population stat.ml stat.th study type