| Name | E-mail (@cs.nyu.edu) | |
|---|---|---|
| Instructor | David Sontag | dsontag |
| Instructor | Joan Bruna | bruna |
| TA | Rahul Krishnan | rahul |
| Grader | Aahlad Manas | apm470 {@/at} nyu.edu |
| Grader | Alex Nowak | anv273 {@/at} nyu.edu |
##Syllabus This graduate level course presents fundamental tools of probabilistic graphical models, with an emphasis on designing and manipulating generative models, and performing inferential tasks when applied to various types of data.
We will study latent variable graphical models (Latent Dirichlet Allocation, Factor Analysis, Gaussian Processes), state-space models for time series (Kalman Filter, HMMs, ARMA), Gibbs Models, Deep generative models (Variational autoencoders, GANs), and causal inference, covering both the methods (exact/approximate inference, sampling algorithms, exponential families) and modeling applications to text, images and medical data.
###Lecture Location Monday, 5:10-7:00pm, in Warren Weaver Hall 1302 ###Recitation/Laboratory (required for all students) Wednesdays, 7:10-8:00pm in Meyer Hall of Physics 121
###Office hours DS: Mondays, 10:00-11:00am. Location: 715 Broadway, 12th floor, room 1204.
JB: Thursdays, 4:00-5:00pm. Location: 60 5th ave, 6th floor, room 612.
###Grading problem sets (45%) + midterm exam (25%) + final project (25%) + participation (5%).
###Piazza We will use Piazza to answer questions and post announcements about the course. Please sign up here. Students' use of Piazza, particularly for adequately answering other students' questions, will contribute toward their participation grade.
###Online recordings Most of the lectures and labs' videos will be posted to NYU Classes. Note, however, that class attendance is required.
##Schedule
| Week | Lecture Date | Topic | Reference | Deliverables |
|---|---|---|---|---|
| 2 | 9/12 | Lec1 Intro and Logistics. Bayesian Networks. Slides | Murphy Chapter 1 (optional; review for most) Notes on Bayesian networks (Sec. 2.1) Algorithm for d-separation (optional) |
PS1, due 9/19 |
| 3 | 9/19 | Lec2 Undirected Graphical Models. Markov Random Fields. Ising Model. Applications to Statistical Physics. Slides | Notes on MRFs (Sec. 2.2-2.4) Notes on exponential families |
PS2 [data], due 9/26 |
| 4 | 9/26 | Lec3 Introduction to Inference. Variable elimination. Slides | Murphy Sec. 20.3 Notes on variable elimination (optional) |
PS3 [data], due 10/3 |
| 5 | 10/3 | Lec4 Modeling Text Data. Topic Models. Latent Dirichlet Allocation. Gibbs sampling. Slides | Barber 27.1-27.3.1 Murphy Sec. 24.1-24.2.4 Introduction to Probabilistic Topic Models Explore topic models of: politics over time, state-of-the-union addresses, Wikipedia |
PS4, due 10/17 Project Proposal, due 10/24 |
| 6 | 10/10 | No lecture (there is lab). | ||
| 7 | 10/17 | Lec5 Modeling Survey Data. Factor Analysis. PCA. ICA. Slides | Elements of Statistical Learning, Ch.14 Finding Structure in Randomness (...), Halko, Martinsson, Tropp |
PS5, due 10/24 |
| 8 | 10/24 | Lec6 Clustering. EM. Markov Chain Monte-Carlo (MCMC). slides | MIT Lecture 18 Notes Elements of Stat. Learning 14.5 and 8.5 Hamilton Monte-Carlo (optional) |
|
| 9 | 10/31 | Midterm Exam | ||
| 10 | 11/7 | Lec7 Variational Inference. Revisiting EM. Mean Field. slides | Graphical Models, Exponential Families and Variational INference, Chapter 3 Variational INference with Stochastic Search | |
| 11 | 11/14 | Lec8 Modeling Time Series Data. Spatial and Spectral models. GPs, ARMA, HMMs, RNNs. slides | Shumway&Stoffer, Chapters 2, 3 and 6. Lecture notes Stat 153 JB |
PS6, due 11/21 |
| 12 | 11/21 | Lec9 Modeling Structured Outputs and Conditional Random Fields (CRFs). slides Exponential families, maximum likelihood estimation, moment matching, maximum entropy, pseudo-likelihood. No lab this week |
||
| 13 | 11/28 | Lec10 Structured Outputs (contd). Dual Decomposition. Integer Linear Programming. Structured SVM. Deep Structured Prediction. | PS7, due 12/5 | |
| 14 | 12/5 | Lec11 Causal Inference. | ||
| 15 | 12/12 | Lec12 Modeling Images and high-dimensional data. Boltzmann Machines. Autoencoders. Variational Autoencoders. | ||
| 12/13 | Lec13 Modeling Images and high-dimensional data (contd). Deep Auto-regressive Models. Generative Adversarial Networks (GANs). | Project writeup, due 12/16. | ||
| 16 | 12/19 | Final Day Poster Presentations of Final Projects |
###Bibliography There is no required book. Assigned readings will come from freely-available online material.
- Kevin Murphy, Machine Learning: a Probabilistic Perspective, MIT Press, 2012. You can read this online for free from NYU Libraries. We recommend the latest (4th) printing, as earlier editions had many typos. You can tell which printing you have as follows: check the inside cover, below the "Library of Congress" information. If it says "10 9 8 ... 4" you've got the (correct) fourth print.
- Daphne Koller and Nir Friedman, Probabilistic Graphical Models: Principles and Techniques, MIT Press, 2009.
- Mike Jordan's notes on Probabilistic Graphical Models
- MIT lecture notes on algorithms for inference.
- Probabilistic Programming and Bayesian Methods for Hackers by Cam Davidson Pilon
- Trevor Hastie, Rob Tibshirani, and Jerry Friedman, Elements of Statistical Learning, Second Edition, Springer, 2009. (Can be downloaded as PDF file.)6
- David Barber, Bayesian Reasoning and Machine Learning , Cambridge University Press, 2012. (Can be downloaded as PDF file.)
- Review notes from Stanford's machine learning class
- Sam Roweis's probability review
- Convex Optimization by Stephen Boyd and Lieven Vandenberghe.
- Mike Jordan and Martin Wainwright, Graphical Models, Exponential Families, and Variational Inference
- Shumway and Stoffer Time Series Analysis and its Applications: with R examples
We expect you to try solving each problem set on your own. However, when being stuck on a problem, we encourage you to collaborate with other students in the class, subject to the following rules:
- You may discuss a problem with any student in this class, and work together on solving it. This can involve brainstorming and verbally discussing the problem, going together through possible solutions, but should not involve one student telling another a complete solution.
- Once you solve the homework, you must write up your solutions on your own, without looking at other people's write-ups or giving your write-up to others.
- In your solution for each problem, you must write down the names of any person with whom you discussed it. This will not affect your grade.
- Do not consult solution manuals or other people's solutions from similar courses.
During the semester you are allowed at most two extensions on the homework assignment. Each extension is for at most 48 hours and carries a penalty of 25% off your assignment.