26. Gaussian Mixture Models

A Gaussian mixture model (GMM) is a family of multimodal probability distributions, which is a plausible generative model for clustered data. We can fit this model using maximum likelihood, and we can assess the quality of fit by evaluating the model likelihood on holdout data. While the "learning" phase of Gaussian mixture modeling is fitting the model to data, in the "inference" phase, we determine for any point drawn from the GMM the probability that it came from each of the k components. To use a GMM for clustering, we simply assign each point to the component that it is most likely to have come from. k-means clustering can be seen as a limiting case of a restricted form of Gaussian mixture modeling.
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