Handbook

This course presents an in-depth study of statistical machine learning approaches. It aims to provide the student with a solid understanding of methods for learning and inference in structured probabilistic models, with a healthy balance of theory and practice. It will cover topics on the semantics of direct and undirected representations in probabilistic graphical models, exact and approximate inference, and learning of model parameters and structure.

In this course, we will study a class of statistical inference models known as Probabilistic Graphical Models (PGMs). PGMs are a great example of how Computer Science and Statistics can work together. PGMs use graph data structures to represent domains with large amounts of variables and specialised algorithms for efficient inference over these graphical models. Therefore, PGMs have pushed the limits of probability theory to the scale and rate necessary to provide automated reasoning in modern AI systems.

During this course, we will cover several graphical models, including Bayesian networks, Markov networks, Conditional Random Fields, Markov chains, Hidden Markov Models, Kalman Filters and Markov decision processes. We will have a clear understanding of how these models work as well as their main algorithms for inference and learning. We will also cover several algorithms used to learn parameters and make inferences such as Monte Carlo Markov Chains (MCMC), Gibbs Sampling, Viterbi and the Baum-Welch algorithms, among others.