Maximum number of modes of Gaussian mixtures

Carlos Amendola*, Alexander Engstrom, Christian Haase

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


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.

Original languageEnglish
Pages (from-to)587-600
Number of pages14
JournalInformation and Inference: a Journal of the IMA
Issue number3
Publication statusPublished - Sep 2020
MoE publication typeA1 Journal article-refereed


  • Gaussian density
  • mixture distribution
  • local maxima
  • clustering

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