Graphical Models: Discrete Inference and Learning

Karteek Alahari, Demian Wassermann

Graphical models (or probabilistic graphical models) provide a powerful paradigm to jointly exploit probability theory and graph theory for solving complex real-world problems. They form an indispensable component in several research areas, such as statistics, machine learning, computer vision, where a graph expresses the conditional (probabilistic) dependence among random variables.

This course will focus on discrete models, that is, cases where the random variables of the graphical models are discrete. After an introduction to the basics of graphical models, the course will then focus on problems in representation, inference, and learning of graphical models. We will cover classical as well as state of the art algorithms used for these problems. Several applications in machine learning and computer vision will be studied as part of the course.

All the classes will be held at the Gif-sur-Yvette campus of CentraleSupelec, unless mentioned otherwise below.

Mailing list: All announcements (last-minute changes, projects, etc.) will be made on a dedicated mailing list. Everyone who registered for the course has already been added to this list. If you are new, and would like to subscribe to the list, visit:

11/113:45 - 17:00Microsoft TeamsIntroduction [slides]
Graphical Models [slides]
18/113:45 - 17:00Amphi F2.07Relaxation, Primal-dual methods [slides]
25/113:45 - 17:00Microsoft TeamsBelief propagation [slides]
Graph cuts - intro [slides]
01/213:45 - 17:00Amphi F2.07
22/213:45 - 17:00Microsoft TeamsGraph Cuts [slides]
01/313:45 - 17:00Microsoft TeamsGraph Cuts (contd.), Bayesian Nets [slides]
08/313:45 - 17:00Amphi F2.07Causality and other topics [slides]
01/410:30 - 17:00Amphi E2.19 (Janet), BreguetProject presentations

Probabilistic graphical models: principles and techniques, Daphne Koller and Nir Friedman, MIT Press
Convex Optimization, Stephen Boyd and Lieven Vanderbeghe
Numerical Optimization, Jorge Nocedal and Stephen J. Wright
Introduction to Operations Research, Frederick S. Hillier and Gerald J. Lieberman
An Analysis of Convex Relaxations for MAP Estimation of Discrete MRFs, M. Pawan Kumar, Vladimir Kolmogorov and Phil Torr
Convergent Tree-reweighted Message Passing for Energy Minimization, Vladimir Kolmogorov
An Introduction to Lifted Probabilistic Inference