expectation maximization

EM is the classic latent-variable algorithm, and a GMM is how it appears in practice. What interviewers reward is the E-step/M-step alternation, why it is soft clustering where k-means is hard, and the honest caveat that it only reaches a local optimum. Here is the answer.

A Gaussian mixture trained by EM has a well-known trap: one Gaussian shrinks onto a single point and the likelihood races to infinity. Understanding the cause, plus the three standard remedies, tells apart people who merely ran sklearn from those who grasp it.