Maximum Number of Modes of Gaussian Mixtures

Abstract

Gaussian mixture models are widely used in Statistics. A fundamental aspect of these distributions is the study of the local maxima of the density, or modes. In particular, it is not known how many modes a mixture of $k$ Gaussians in $d$ dimensions can have. We give a brief account of this problem's history. Then, we give improved lower bounds and the first upper bound on the maximum number of modes, provided it is finite.

14 pages, 5 figures. Final version, to appear in Information and Inference

References in corpus (1)

• The topography of multivariate normal mixtures

Cited by in corpus (2)

• Fast approximations of the Jeffreys divergence between univariate Gaussian mixture models via exponential polynomial densities
• A fast and efficient Modal EM algorithm for Gaussian mixtures