Introduction to Graphical Models

Guillaume Obozinski - Simon Lacoste-Julien - 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, 2015/2016

Please Register for the class (mandatory to access the homework).
 - Please fill out this form to register by Friday October 2nd NOON; extension to Wednesday Oct 14th 9am.

[Note that filling the form does not bind you to take the class for credit; it is just so that we can create an account for you to access the material on the moodle.]
This year, the class will be taught in English. All homework should be submitted in English.

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
September 30th
Guillaume Obozinski Introduction
Maximum likelihood
Slides (intro)
Slides ML
Huu Dien Khue Le, Robin Benesse
October 7th
Guillaume Obozinski Linear regression
Logistic regression
Generative classification (Fisher discriminant)
Gaussian mixtures
6, 7
Slides Regression
10, 11
Slides EM
Aymeric Reshef, Claire Vernade
Marie d’Autume, Jean-Baptiste Alayrac
October 14th
Simon Lacoste-Julien Graph theory
Directed graphical models
Undirected graphical models
Jaime Roquero, JieYing Wu
(updated 11/29)
October 21st
Simon Lacoste-Julien Exponential families
Information theory
8, 19
scribbled notes
Thomas Belhalfaoui, Lénaïc Chizat
October 28th
Francis Bach Gaussian variables
Factor analysis
13, 14
Lucas Plaetevoet, Ismael Belghiti
November 4th
Simon Lacoste-Julien Sum-product algorithm
4, 12
scribbled notes
Pauline Luc, Mathieu Andreux
November 11th

No lecture

November 18th
Guillaume Obozinski Approximate inference I
Variational inference
Khalife Sammy, Maryan Morel
(new!) lecture8.pdf
November 25th
Guillaume Obozinski Approximate inference II
Variational inference
Basile Clément, Nathan de Lara
(new!) lecture9.pdf
December 2nd
Simon Lacoste-Julien Bayesian methods
Model selection
5.1 and 5.3
scribbled notes
Gauthier Gidel, Lilian Besson
(new!) lecture10.pdf
December 16th
(Amphi Curie)
Final Exam
January 6th
Batiment Cournot (C102-103)
Project poster session

Homework (tentative schedule)

Homework 1, due October 24th, 2015 (on the Moodle): Homework | Data.

Homework 2, due November 11th, 2015 (on the Moodle): Homework | Data

Homework 3, due January 6th, 2016 (on the Moodle; we highly recommend you submit it in December though): Homework | Data


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 (one or two students per projects, preferably two)
Before 11/18 Send an email to the three teachers, in which all members of your team are cc'ed to request our agreement on your choice of team and project topic.
Before 12/09 Send a draft (1 page) + first results, on the Moodle.
On 2016/01/06 Poster session in Batiment Cournot (C102-103) - 9am to 12pm
Before 2016/01/13 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 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: December 2nd, 2015.