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Inference and Representation (DS-GA-1005, CSCI-GA.2569)

Course staff:

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Name E-mail
Instructor Joan Bruna [email protected]
TA Vlad Kobzar [email protected]

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 graphical models (Latent Dirichlet Allocation, Gaussian Processes), state-space models for (Kalman Filter, HMMs), Gibbs Models, Deep generative models (Variational autoencoders, GANs) covering both the methods (inference, sampling algorithms, learning, exponential families) and modeling applications to text, images and physics data.

Lecture Location

Monday, 6:20-8:00pm, in 60 FA 110

Recitation/Laboratory (required for all students)

Wednesdays, 5:20-6:10pm in 60 FA 110

Office hours

JB: Monday, 10:00-11:00pm. 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. 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 9/11 Lec1 Introduction and Logistics. Inference Examples. Bayesian Networks. Slides Murphy Chapter 1 (optional; review for most)

Notes on Bayesian networks (Sec. 2.1)

Algorithm for d-separation (optional)
PS1, due 9/18
3 9/18 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

Notes on Hammersley-Clifford Theorem
PS2 [data], due 9/25
4 9/25 Guest Lecture Kyle Cranmer (NYU): Likelihood-free Inference Slides
5 10/2 Lec3 Belief-Propagation. 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
PS3, due 10/17

Project Proposal, due 10/23
6 10/9 Lec4 PCA. ICA. Applications to Survey Data Slides Elements of Statistical Learning, Ch.14

Finding Structure in Randomness (...), Halko, Martinsson, Tropp
PS4, due 10/24
7 10/16 Lec5 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)
8 10/23 Guest Lecture TBA
9 10/30 Midterm Exam
10 11/6 Lec6 Variational Inference. Revisiting EM. Mean Field. slides Graphical Models, Exponential Families and Variational INference, Chapter 3 Variational INference with Stochastic Search
12 11/13 Lec7 Structured Output Prediction. Conditional Random Fields (CRF), Hidden Markov Models, Moment Matching PS5, due 11/21
13 11/20 Lec8 Sequential Models slides

No lab this week
Murphy, Secs. 19.5 & 19.6
Notes on pseudo-likelihood
An Introduction to Conditional Random Fields (section 4; optional)
Approximate maximum entropy learning in MRFs (optional)
14 11/27 Lec9 Boltzmann Machines. Variational Autoencoders slides PS6, due 12/5
15 12/4 Guest Lecture TBA
16 12/11 Lec10 Modeling Images and high-dimensional data. Deep Auto-regressive Models. Normalizing Flows. Generative Adversarial Networks references in slides
12/12 Lec11 Further applications of GANS. Open Problems references in slides Project writeup, due 12/16.
17 12/18 Final Day Poster Presentations of Final Projects

Location: Center for Data Science, 60 5th ave, in the 7th floor open space

Bibliography

There is no required book. Assigned readings will come from freely-available online material.

Core Materials

Background on Probability and Optimization

Further Reading

Academic Honesty

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.

Late submission policy

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.

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