## 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 \(\Pr(\mathbf{x})= \sum_{k=1}^{K}\pi_k\mathcal{N}(\mathbf{x}|\mathbf{\mu}_k,\Sigma_k)\): - the parameters of Gaussian: \(\mathbf{\mu}_k,\Sigma_k\) - and latent variables: \(\mathbf{z}\)...