## 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: $$\mathbf{z}$$...

March 5, 2020 · (Last Modification: April 28, 2022) · Anthony Tan