Maximum number of modes of Gaussian mixtures
Carlos Améndola, Alexander Engström, Christian Haase · Information and Inference A Journal of the IMA · 2019
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.