Maximum number of modes of Gaussian mixtures-Reference-Cited by-同舟云学术

Maximum number of modes of Gaussian mixtures

Published:2019-06-29 Issue:3 Volume:9 Page:587-600
ISSN:2049-8772
Container-title:Information and Inference: A Journal of the IMA
language:en
Short-container-title:

Author:

Améndola Carlos¹,Engström Alexander²,Haase Christian³

Affiliation:

1. Department of Mathematics, Technical University of Munich, 85748, Garching (b. Munich), Germany

2. Department of Mathematics, Aalto University, 00076, Aalto, Finland

3. Department of Mathematics, Free University Berlin, 14195, Berlin, Germany

Abstract

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 $k$ 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.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Numerical Analysis,Statistics and Probability,Analysis

Link

http://academic.oup.com/imaiai/article-pdf/9/3/587/33720702/iaz013.pdf

Reference18 articles.

1. On the number of modes of finite mixtures of elliptical distributions;Alexandrovich,2013

2. Maximum likelihood estimates for gaussian mixtures are transcendental;Améndola,2015

3. On the modes of a mixture of two normal distributions;Behboodian;Technometrics,1970

4. Théorie générale des équations algébriques;Bézout,1779

5. Algebraic Complexity Theory

Cited by 15 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Convergence Analysis of Mean Shift;IEEE Transactions on Pattern Analysis and Machine Intelligence;2024-10

2. Multivariate, heteroscedastic empirical Bayes via nonparametric maximum likelihood;Journal of the Royal Statistical Society Series B: Statistical Methodology;2024-05-29

3. Metal artefact reduction in digital tomosynthesis using component decomposition;Biomedical Physics & Engineering Express;2023-01-24

4. GMM-IL: Image Classification Using Incrementally Learnt, Independent Probabilistic Models for Small Sample Sizes;IEEE Access;2023

5. Towards Benchmark Data Generation for Feature Tracking in Scalar Fields;2022 Topological Data Analysis and Visualization (TopoInVis);2022-10