Intelligent Systems: Machine Learning seminars

This video is a lecture from a machine learning course on intelligent systems. It begins with a review of Bayesian logistic regression, including the approximation of the posterior distribution and the importance of uncertainty in predictions. The discussion then covers handling missing data, highlighting the pitfalls of simple imputation methods like mean or median replacement. The lecturer explains that proper Bayesian treatment involves modelling the distribution of missing values conditioned on observed data, and then integrating over them. The main focus then shifts to the Expectation-Maximization (EM) algorithm. The lecture explains the general framework where we have observed variables, latent variables, and model parameters, and we want to maximize the marginal likelihood. The EM algorithm iterates between an E-step, where we compute the expected value of the log-likelihood over the latent variables given current parameters, and an M-step, where we maximize this expectation with respect to the parameters. The lecture shows how EM can be applied to problems like Gaussian mixtures and how it relates to variational inference. The variational EM algorithm is introduced as a generalization for cases where the posterior is intractable. Throughout, the emphasis is on understanding uncertainty and proper Bayesian reasoning.