Gaussian mixture

In Chapter 2, Introduction to Semi-Supervised Learning, we discussed the generative Gaussian mixture model in the context of semi-supervised learning. In this paragraph, we're going to apply the EM algorithm to derive the formulas for the parameter updates.

Let's start considering a dataset, X, drawn from a data generating process, pdata:

We assume that the whole distribution is generated by the sum of k Gaussian distributions so that the probability of each sample can be expressed as follows:

In the previous expression, the ...

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