Maximum Likelihood of Gaussian Mixtures

Preliminaries Probability Theory multiplication principle joint distribution the Bayesian theory Gaussian distribution log-likelihood function ‘Maximum Likelihood Estimation’ Maximum Likelihood1 Gaussian mixtures had been discussed in ‘Mixtures of Gaussians’. And once we have a training data set and a certain hypothesis, what we should do next is estimate the parameters of the model. Both kinds of parameters from a mixture of Gaussians (Pr(mathbf{x})= sum_{k=1}^{K}pi_kmathcal{N}(mathbf{x}|mathbf{mu}_k,Sigma_k)): – the parameters of Gaussian: (mathbf{mu}_k,Sigma_k) – and latent variables: (mathbf{z})