Introduction to Graphical Models

Guillaume Obozinski - Francis Bach
Ecole des Ponts, ParisTech - INRIA/ENS - INRIA/ENS

Master recherche specialite "Mathematiques Appliquees",
Parcours M2 Mathematiques, Vision et Apprentissage (ENS Cachan), 1er semestre, 2016/2017

This year, the class will be taught in English. Homeworks and project may be submitted in English or in French.

Classes will take place on Wednesdays from 9am to 12pm at ENS Cachan, in Amphi Curie.

Moodle for the class.

Dates of classes

Below is the tentative schedule, with scribe notes from last year that might be updated for some lectures.

Date Lecturer Topics Corresponding chapters in class notes Scribe notes
October 5th
Guillaume Obozinski Introduction
Maximum likelihood
Slides (intro)
Slides ML
Huu Dien Khue Le, Robin Benesse
October 12th
Guillaume Obozinski Linear regression
Logistic regression
Generative classification (Fisher discriminant)
6, 7
Slides Regression
Aymeric Reshef, Claire Vernade
October 19th
Guillaume Obozinski K-means
Gaussian mixtures
10, 11
Slides EM
Marie d'Autume, Jean-Baptiste Alayrac
October 26th
Francis Bach Graph theory
Directed graphical models
Undirected graphical models
Jaime Roquero, JieYing Wu
November 2nd
Francis Bach Exponential families
Information theory
8, 19
Thomas Belhalfaoui, L&eacutena&iumlc Chizat
November 9th
Francis Bach Gaussian variables
Factor analysis
13, 14
Lucas Plaetevoet, Ismael Belghiti
November 16th
Guillaume Obozinski Sum-product algorithm
4, 12
Pauline Luc, Mathieu Andreux
November 23rd
Guillaume Obozinski Approximate inference
Variational inference
Khalife Sammy, Maryan Morel
Basile Cl&eacutement, Nathan de Lara
November 30th
Francis Bach Bayesian methods
Model selection
5.1 and 5.3
Gauthier Gidel, Lilian Besson
December 14th
(Amphi Curie)

Final Exam

January 4th
Batiment Cournot (C102-103)

Project poster session

Homework (tentative schedule)

Homework 1, due October 31st, 2016 (on the Moodle): Homework | Data.


Updated page with current project proposals.

The final project allows a further understanding of certain aspects of the course. The following schedule has to be respected.

November Choose a project and form teams of three.
Before 2016/11/18 Send an email to the two teachers, in which all members of your team are cc'ed to request our agreement on your choice of team and project topic.
Before 2016/12/09 Submit a progress report of 1 page including first results, on the Moodle.
On 2017/01/04 Poster session in Batiment Cournot (C102-103) - 9am to 12pm
Before 2016/01/11 Submit your project report (~6 pages, on the Moodle)


This course provides a unifying introduction to probabilistic modelling through the framework of graphical models, together with their associated learning and inference algorithms.

References - Class notes

The course will be based on the book in preparation of Michael I. Jordan (UC Berkeley). Printed version of parts of the book (playing the role of the "polycopie") will be available from the Master's administrative assistant one or two weeks after the beginning of classes. We will notify you when they are ready for you to go and pick them up.

Last updated: November 8th, 2016.