IFT 6269 : Probabilistic Graphical Models - Fall 2021

Last year version: Fall 2020
Next year version: Fall 2022

Description

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

People

Class info (hybrid lectures)

The lectures are taught in hybrid mode: the lectures will be given at the Mila Agora, 6650 rue Saint-Urbain, but also connected synchronously on Zoom (see info on Studium). They will also be recorded for further review or for those in remote time zones.

Tentative content

(Detailed outline below)

Evaluation

Prerequisites

Textbook

Homework logistics

Detailed outline (updated often)

Below is a draft detailed outline that will be updated as the class goes on. For now it is the outline recopied from the Fall 2020 version of this class, with the links to the relevant old scribbled notes that will be updated with the new ones gradually. The related chapters in Mike's book are given (but note that they do not exactly correspond with the class content), and also sometimes pointers to the Koller and Friedman book (KF), the Deep Learning book (DL) or the Bishop's book (B). Related past ‘‘scribe notes’’ from the previous instantiations of this class as well as (for later lectures) the class that I taught in Paris are given for now, and will be updated with the more updated scribe notes if needed (and I get some).

Date Topics Related chapters
Scribbled notes
Recordings
Scribe notes Homework milestones
Sept 3 (Fri) Set-up & overview lecture1
recording
Isabela Albuquerque (Fa17)
lecture1.pdf
source
Sept 7 (Tu) Probability review 2.1.1
DL: 3 (nice and gentle)
KF: 2.1 (more rigorous)
lecture2
recording
William L├ęchelle (Fa16)
lecture2.pdf
source
Sept 10 (Fri) Prob. review (cont.)
Parametric models
5
lecture3
recording
Philippe Brouillard and Tristan Deleu (Fa17)
lecture3.pdf
source
Hwk 1 out
(hwk 1 source)
Sept 14 (Tu) Frequentist vs. Bayesian
Maximum likelihood
lecture4
recording
Philippe Brouillard and Tristan Deleu (Fa17)
lecture4.pdf
source
Sept 17 (Fri) MLE (cont.)
Statistical decision theory
1.3 in Bickel & Doksum
Bias-variance tradeoff: 7.3 in Hastie's book
lecture5
recording
S├ębastien Lachapelle (Fa17)
lecture5.pdf
source
Sept 21 (Tu) Properties of estimators
and MLE
lecture6
recording
same as lecture5
Sept 24 (Fri) Linear regression
Logistic regression
DL: 7.1 (l2, l1-reg.)
6, 7
lecture7
recording
Zakaria Soliman (Fa16)
lecture6.pdf
source
Sept 28 (Tu) Numerical Optimization
Logistic regression (cted) and IRLS

7
DL: 4.3
Boyd's book
lecture8
recording
Eeshan Gunesh Dhekane and Younes Driouiche (Fa18)
lecture8.pdf
source
Hwk 1 due
Hwk 2 out
data.zip
Oct 1 (Fri) Gen. classification (Fisher)
Derivative tricks for
Gaussian MLE

Kernel trick (skipped)
7
Matrix Diff. book
lecture9

recording

lecture9 2017 (kernel trick) (skipped)
Eeshan Gunesh Dhekane (Fa18)
lecture9.pdf
source
Oct 5 (Tu) latent variable model
K-means
EM
10, 11
lecture10
recording
Ismael Martinez and Binulal Narayanan (Fa20)
lecture12-2020.pdf
source
Oct 8 (Fri) GMM and EM
Graph Theory
10,11
2
lecture11
recording
mix of previous and next lecture
Oct 12 (Tu) Directed Graphical Models 2
lecture12
recording
Martin Weiss and Eeshan Gunesh Dhekane (Fa18)
lecture11.pdf
source
Oct 15 (Fri) DGM (cont.)
Undirected graphical models
2
lecture13
recording
Philippe Beardsell (Fa18)
lecture12.pdf
source
Oct 19 (Tu) Break: look at projects Hwk 2 due
Hwk 3 out
(hwk 3 source)
data.zip
Oct 22 (Fri) Break: look at projects
Oct 26 (Tu) Inference: elimination alg. 3
lecture14
recording
lecture13-2018.pdf
source
Oct 29 (Fri) Sum-product alg.
Max-product
Junction tree
4, 17
lecture15
recording
lecture16-2020.pdf
source
Nov 2 (Tu) HMM and EM 12
lecture16
recording
lecture15-2018.pdf
source
Nov 5 (Fri) Information theory
Max entropy
19
lecture17
recording
lecture15-2018.pdf (above)
lecture16-2018.pdf
source
Nov 9 (Tu) MaxENT duality
Exponential families
8
(KL geometry: lecture 16 2017)
lecture18
recording
lecture16-2018.pdf (above) Hwk 3 due
Hwk 4 out
(hwk 4 source)
Nov 12 (Fri) Exponential families
Estimation in graphical models
8
9
lecture19
recording
MVA lecture5
MVA lecture8
Project: team formed
Nov 16 (Tu) MC integration
Sampling
21
(variance reduction: see old lecture18 2017)
lecture20
recording
Nov 19 (Fri) MCMC
Markov chains
Metropolis-Hastings
21
lecture21
recording
Nov 23 (Tu) Gibbs sampling
Variational methods
Bishop: 10.1
lecture22
recording

(skipped parts of: old lecture22 2017 for marginal polytope)
MVA lecture9
Nov 26 (Fri) Bayesian methods
Model selection

Causality
5, 26
lecture23
recording

Causality for Machine Learning (arXiv 2019)
Elements of Causal Inference (book)
MVA lecture10
Nov 30 (Tu) Gaussian networks

Factor analysis, PCA, CCA
(Kalman filter)
VAE
lecture24
recording

13
old lecture17 Fa2016
14 , (15)
old lecture18 Fa2016
VAE – DL: 20.10.3
MVA lecture6.5
MVA lecture7.3
Hwk 4 due
Hwk 5 out
(hwk 5 source)
Dec 3 (Fri) (Guest lecture on causality by
Sebastien & Tristan)
lecture25
recording
Project: 1 page
progress report due
(skipped) Non-parametric models: Gaussian processes
Dirichlet processes
25
old lecture26
old recording

GP book
DP tutorial
Dec 7 (Tu) No lecture this week (NeurIPS)
work on your project!
Dec 15 (Wed) Poster presentation
2:00pm-5:00pm
Take-home final out
Dec 22 (Wed) Hwk 5 due
Project report due
Take-home final due