Assessing the performance of a Gaussian mixture with AIC and BIC

As a Gaussian mixture is a probabilistic model, finding the optimal number of components requires an approach different from the methods analyzed in the previous chapters. One of the most widely used techniques is the Akaike Information Criterion (AIC), which is based on information theory (presented for the first time in Akaike H., A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19 (6)). If a probabilistic model has np parameters (that is, single values that must be learned) and achieves the maximum negative log-likelihood, Lopt, the AIC is defined as follows:

Such a method has two important implications. The first one is about the ...

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