Last year version: Fall 2019

Newer version: Fall 2021

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.

Teacher: Simon Lacoste-Julien

Office hours: 1-2pm Thursday - on Zoom (see info on Studium)

TA: Jose Gallego

Office hours: 1-2pm Monday - on Zoom (see info on Studium)

Tuesday 14:30-16:30 - on Zoom (see info on Studium)

Friday 13:30-15:30

The lectures will be (synchronous) online on Zoom, but also recorded for further review or for those in remote time zones.

Probability review

Maximum likelihood estimation

Linear regression, logistic regression, Fisher discriminant

K-means, EM, Gaussian mixtures

Directed and undirected graphical models

Exponential family, information theory

Gaussian networks

Factor analysis

Sum-product algorithm, HMM, junction tree

Approximate inference: sampling, variational methods

Estimation of parameters in graphical models

Bayesian methods

Model selection

Homework (40%) – 5 homework | homework logistics below

Project (30%) – project report to hand in + poster presentation on Dec 15th | detailed info about projects

Final exam (30%) – take-home exam, after poster presentation - due Dec 23rd

The prerequisites are previous coursework in linear algebra, multivariate calculus, and basic probability and statistics. There will be programming for the assignments, so familiarity with some matrix-oriented programming language will be useful (we will use Python with numpy).

**Warning:**This class is quite mathematical, and the amount of work is significant (this is a 4 credits class, so expect at least 8 hours of work per week in addition to the lectures), so do not take it if you do not like maths or are looking for an easy class.

The course will follow the (unpublished) manuscript

*An Introduction to Probabilistic Graphical Models*by Michael I. Jordan that will be made available to the students (but do not distribute!).Supplementary references:

For very detailed and rigorous reference: Probabilistic Graphical Models: Principles and Techniques by Daphne Koller and Nir Friedman. Referred as KF in outline below.

See Part I of the Deep Learning book by Ian Goodfellow, Yoshua Bengio and Aaron Courville for a very gentle review of applied maths useful for this class. Chapter 5 contains a useful presentation of machine learning basics. Referred as DL in outline below.

Another classical book, with a more Bayesian perspective than Mike's book, but at least completed, is Pattern Recognition and Machine Learning, by Chris Bishop.

The homework is to be handed online in Studium before

**the beginning of the class**(Tuesday) on the due date. The detailed instructions for the code handin-logistics can be found in the news in Studium.**Collaboration policy**: you can collaborate with colleagues while working on the homework, but you need to write your own independent write-up. And if you have collaborated with others on a question,*you need to credit the help of your colleagues by specifying them in the write-up*(proper acknowledgment is good practice for you have for academia later).**Late homework policy**:You have a budget of 6 late days that you can spend on the 5 homework. To use these days, you need to

*declare it*by filling the appropriate option in the Google form to hand in with the assignment.The late day penalty will be the following (as deadlines are on Tuesday):

handed in Tuesday after beginning of class: 10% penalty (or 1 day late used)

handed in Wednesday: 20% penalty (or 1 day late used)

handed in Thursday: 40% penalty (or 2 days late used)

handed in Friday: 80% penalty (or 3 days late used)

handed in later: you won't get any credit (or you have to have used some of your late days to reduce the number of days counted late)

handed in Monday: 100% penalty (or 4 days late used)

handed in Tuesday (one week later): 100% penalty (or 5 days late used)

**No assignment accepted more than one week late**

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 2019 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 class that I taught in Paris are given for now, and will be updated with the scribe notes as I get them (if I get some).

Date | Topics | Related chapters Scribbled notes Recordings | Scribe notes | Homework milestones |

Sept 1 (Tu) | Set-up & overview | intro slides lecture1 recording | Isabela Albuquerque (Fa17) lecture1.pdf source | |

Sept 4 (Fri) | Probability review | 2.1.1 DL: 3 (nice and gentle) KF: 2.1 (more rigorous) lecture2 recording | William Léchelle (Fa16) lecture2.pdf source | |

Sept 8 (Tu) | Prob. review (cont.) Parametric models | 5 lecture3 recording | Philippe Brouillard and Tristan Deleu (Fa17) lecture3.pdf source | Hwk 1 out (hwk 1 source) |

Sept 11 (Fri) | Frequentist vs. Bayesian Maximum likelihood | lecture4 recording | Philippe Brouillard and Tristan Deleu (Fa17) lecture4.pdf source | |

Sept 15 (Tu) | MLE (cont.) Basic Optimization Bias-Variance Decomposition | 1.3 in Bickel & Doksum Bias-variance tradeoff: 7.3 in Hastie's book lecture5 recording | Sébastien Lachapelle (Fa17) lecture5.pdf source | |

Sept 18 (Fri) | Statistical decision theory | lecture6 recording | same as lecture5 | |

Sept 22 (Tu) | Properties of MLE Linear regression | DL: 7.1 (l2, l1-reg.) 6, 7 lecture7 recording | Zakaria Soliman (Fa16) lecture6.pdf source | Hwk 1 due Hwk 2 out |

Sept 25 (Fri) | Ridge regression Logistic regression | 7 lecture8 recording | Eeshan Gunesh Dhekane and Younes Driouiche (Fa18) lecture8.pdf source | |

Sept 29 (Tu) | Numerical Optimization Logistic regression (cted) + IRLS | 7 DL: 4.3 Boyd's book lecture9 recording | same as lecture8 | |

Oct 2 (Fri) | Gen. classification (Fisher) Derivative tricks for Gaussian MLE Kernel trick (skipped) | 7 Matrix Diff. book lecture10 recording lecture9 2017 (kernel trick) (skipped) | Eeshan Gunesh Dhekane (Fa18) lecture9.pdf source | |

Oct 6 (Tu) | latent variable model K-means | 10 lecture11 recording | same as lecture9 | |

Oct 9 (Fri) | GMM and EM | 10,11 lecture12 recording part I recording part II | Ismael Martinez and Binulal Narayanan (Fa20) lecture12-2020.pdf source | |

Oct 13 (Tu) | Graph theory Directed Graphical Models | 2 lecture13 recording | Martin Weiss and Eeshan Gunesh Dhekane (Fa18) lecture11.pdf source | Hwk 2 due Hwk 3 out (hwk 3 source) data.zip |

Oct 16 (Fri) | DGM (cont.) Undirected graphical models | 2 lecture14 recording | Philippe Beardsell (Fa18) lecture12.pdf source | |

Oct 20 (Tu) | Break: look at projects | |||

Oct 23 (Fri) | Break: look at projects | |||

Oct 27 (Tu) | UGM (cont.) | 2 lecture15 recording | same as lecture12 | |

Oct 30 (Fri) | Inference: elimination alg. Sum-product alg. | 3, 4 lecture16 recording | lecture13-2018.pdf source lecture16-2020.pdf source | |

Nov 3 (Tu) | Max-product junction tree HMM | 17, 12 lecture17 recording | lecture16-2020.pdf (above) lecture15-2018.pdf source | Hwk 3 due Hwk 4 out (hwk 4 source) |

Nov 6 (Fri) | EM for HMM Information theory | 19 lecture18 (corrected) recording | lecture15-2018.pdf (above) lecture16-2018.pdf source | |

Nov 10 (Tu) | Max entropy MaxENT duality | 8 (KL geometry: lecture 16 2017) lecture19 recording | lecture16-2018.pdf (above) | Project: team formed |

Nov 13 (Fri) | Exponential families Estimation in graphical models | 8 9 lecture20 recording | MVA lecture5 MVA lecture8 | |

Nov 17 (Tu) | MC integration Sampling | 21 (variance reduction: see old lecture18 2017) lecture21 recording | ||

Nov 20 (Fri) | MCMC Markov chains Metropolis-Hastings | 21 lecture22 recording | ||

Nov 24 (Tu) | Gibbs sampling Variational methods | Bishop: 10.1 lecture23 recording (skipped parts of: old lecture22 2017 for marginal polytope) | MVA lecture9 | Hwk 4 due Hwk 5 out (hwk 5 source) |

Nov 27 (Fri) | Bayesian methods Model selection Causality | 5, 26 lecture24 recording Causality for Machine Learning (arXiv 2019) Elements of Causal Inference (book) | MVA lecture10 | |

Dec 1 (Tu) | Gaussian networks Factor analysis, PCA, CCA (Kalman filter) VAE | lecture25 recording 13 old lecture17 Fa2016 14 , (15) old lecture18 Fa2016 VAE – DL: 20.10.3 | MVA lecture6.5 MVA lecture7.3 | Project: 1 page progress report due |

Dec 4 (Fri) | (Jose's lecture) Non-parametric models: Gaussian processes Dirichlet processes | 25 lecture26 recording GP book DP tutorial | ||

Dec 8 (Tu) | No lecture this week (NeurIPS) work on your project! | |||

Dec 15 (Tu) | Poster presentation 2:00pm-5:00pm online on Gather.town | Take-home final out (not graded) | ||

Dec 23 (Wed) | Hwk 5 due Project report due | |||