Python Data Science Handbook [PDF]

Summary
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Python Data Science Handbook

The fact that GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.

A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the likelihood of the data under the model, using cross-validation to avoid overfitting.

Another means of correcting for overfitting is to adjust the model likelihoods using some analytic criterion such as the Akaike information criterion (AIC) or the Bayesian information criterion (BIC).

Scikit-Learn’s GMM estimator actually includes built-in methods that compute both of these, and so it is very easy to operate on this approach.