Overview
Gaussian Mixture Models (GMM) are models that represent normally distributed subpopulations where each population may have different parameters (mean and variance) and for each element in the population we don’t know a priori which subpopulation that data element belongs to.
For example, suppose that our population consists of the height of adults in the population. We can model this by a GMM with two components, corresponding to the subpopulations of men and women. E.g. suppose that men’s heights are normally distributed with mean 69.2 inches and standard deviation 1.2, while women’s heights are normally distributed with mean 63.6 and standard deviation 1.1.
In fact, the model doesn’t know in advance any of these parameters, just that there are two components and each of these subpopulations are normally distributed.
GMM can be viewed as a machine learning method which uses unsupervised learning. It is often used for cluster analysis with advantages over k-means clustering.
Topics
- Univariate GMM
- Multivariate GMM
- Real Statistic support and examples
Under construction
References
McGonagle, J. et al (2024) Gaussian mixture model
https://brilliant.org/wiki/gaussian-mixture-model/
Carrasco, O. C. and Whitfield, B. (2024) Gaussian mixture models explained
https://builtin.com/articles/gaussian-mixture-model
GeeksforGeeks (2023) Gaussian mixture model
https://www.geeksforgeeks.org/gaussian-mixture-model/
Apgar, V. (2023) 3 use-cases for Gaussian Mixture Models (GMM)
https://towardsdatascience.com/3-use-cases-for-gaussian-mixture-model-gmm-72951fcf8363