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.
|Number of pages||14|
|Journal||Information and Inference: a Journal of the IMA|
|Publication status||Published - Sep 2020|
|MoE publication type||A1 Journal article-refereed|
- Gaussian density
- mixture distribution
- local maxima