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Gaussian mixture models and the EM algorithm

Gaussian mixture models and the EM algorithmRamesh Sridharan These notes give a short introduction to Gaussian mixture models (GMMs) and theExpectation-Maximization (EM) algorithm , first for the specific case of GMMs, and thenmore generally. These notes assume you re familiar with basic probability and basic you re interested in the full derivation (Section 3), some familiarity with entropy and KLdivergence is useful but not strictly notation here is borrowed fromIntroduction to Probabilityby Bertsekas & Tsitsiklis:random variables are represented with capital letters, values they take are represented withlowercase letters,pXrepresents a probability distribution for random variableX, andpX(x)represents the probability of valuex(according topX).

A Gaussian mixture model (GMM) is useful for modeling data that comes from one of several groups: the groups might be di erent from each other, but data points within the same group can be well-modeled by a Gaussian distribution. ... the other will follow almost the same process.

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