English

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 kk Gaussians in dd 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