Maximum Number of Modes of Gaussian Mixtures
Statistics Theory
2019-07-22 v3 Optimization and Control
Probability
Statistics Theory
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 Gaussians in 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.
Keywords
Cite
@article{arxiv.1702.05066,
title = {Maximum Number of Modes of Gaussian Mixtures},
author = {Carlos Améndola and Alexander Engström and Christian Haase},
journal= {arXiv preprint arXiv:1702.05066},
year = {2019}
}
Comments
14 pages, 5 figures. Final version, to appear in Information and Inference