When applying the Expectation-Maximization (EM) algorithm to Gaussian Mixture Models (GMMs), what is the primary objective of maximizing the log-likelihood function?
Question 2
In the context of Gaussian Mixture Models, what is the significance of the 'soft assignment' of data points to components during the E-step?
Question 3
Consider a Gaussian Mixture Model where one of the components has a very high mixing coefficient ($\pi_k$) but a very small variance ($\Sigma_k$). What does this configuration suggest about the data points associated with this component?
Question 4
Which of the following describes a key challenge when initializing the parameters for a Gaussian Mixture Model before running the Expectation-Maximization (EM) algorithm?
Question 5
Given a dataset with two distinct, non-spherical clusters that are oriented differently, which type of covariance matrix would be most appropriate for the Gaussian components in a GMM to effectively model this data?
