# Maximum Number of Modes of Gaussian Mixtures

arXiv: https://arxiv.org/abs/1702.05066 · HTML: https://mlsanity.com/paper/1702.05066/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2017.

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## Abstract (arXiv)

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.