Maximum number of modes of Gaussian mixtures

By Carlos Am'endola, Alexander Engstrom, Christian Haase. 2017

35 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jung-Woo Ha
2. Byoung-Tak Zhang
3. Jin-Hwa Kim
4. Jaehyun Jun
5. Sang-Woo Lee
6. Tinne Tuytelaars
7. Rahaf Aljundi
8. Bing Liu

In Statistical and Nonlinear Physics

1. Jung-Woo Ha

In Statistics and Probability

1. Byoung-Tak Zhang
2. Jin-Hwa Kim
3. Jung-Woo Ha
4. Jaehyun Jun
5. Sang-Woo Lee

Citations in the corpus

• Overcoming Catastrophic Forgetting by Incremental Moment Matching (2017, background): “There is a guess that, for all D,K ≥ 1, the upper bound is D + K − 1 choose D [29].”