Summary
In this chapter, we presented the EM algorithm, explaining the reasons that justify its application in many statistical learning contexts. We also discussed the fundamental role of hidden (latent) variables, in order to derive an expression that is easier to maximize (the Q function).
We applied the EM algorithm to solve a simple parameter estimation problem and afterward to prove the Gaussian Mixture estimation formulas. We showed how it's possible to employ the Scikit-Learn implementation instead of writing the whole procedure from scratch (like in Chapter 2, Introduction to Semi-Supervised Learning).
Afterward, we analyzed three different approaches to component extraction. FA assumes that we have a small number of Gaussian latent variables and a Gaussian decorrelated noise term. The only restriction on the noise is to have a diagonal covariance matrix, so two different scenarios are possible. When we are in the presence of heteroscedastic noise, the process is an actual FA. When...
