Topics in Probabilistic Modeling and Inference
CS698X
2017-18 (even semester)
Instructor: Piyush Rai: (office: RM-502, email: piyush AT cse DOT iitk DOT ac DOT in)
Office Hours: Wednesday 11:00am-12:00pm (or by appointment)
Q/A Forum: Piazza
Class Venue: KD-101
Class Timings: T/Th 5:10-6:30pm
TAs: Shivam Bansal, Smrithi Prabhu, Vinay Verma
TA Office Hours: TBD

Background and Course Description

Probabilistic models for data are ubiquitous in many areas of science and engineering, and specific domains such as visual and language understanding, finance, healthcare, biology, climate informatics, etc. This course will be an advanced introduction to probabilistic models of data (often through case studies from these domains) and a deep-dive into advanced inference and optimization methods used to learn such probabilistic models. This is an advanced course and ideally suited for student who are doing research in this area or are interested in doing research in this area.

Pre-requisites

Instructor's consent. The course expects students to have a strong prior background in machine learning (ideally through formal coursework), and ideally also some prior exposure/appreciation to basic principles of probabilistic modeling. The students are expected to have strong foundations in probability and statistics, linear algebra, and optimization, and must also be proficient in programming in MATLAB, Python, or R.

Schedule (Tentative)

Date Topics Readings/References Slides/Notes
Jan 4 Logistics and Introduction to the course Nature article on probabilistic modeling, Probability Refresher slides slides, (print version)
Jan 9 Basics of Probabilistic Modeling and Inference, Single-Parameter Models Parameter Estimation (only up to section 3), BDA Section 1.1-1.3, 1.8, BDA 2.1-2.6 slides, (print version)
Jan 11 Single-Parameter Models (Contd.), Intro to Bayesian Linear Regression BDA 2.1-2.6, MLAPP 7.1-7.3, 7.6 (7.6.1-7.6.2) slides, (print version)
Jan 16 Bayesian Linear Regression (Contd) PRML 3.3, MLAPP 7.1-7.3, 7.6 (7.6.1-7.6.2) slides, (print version)
Jan 18 Learning Hyperparameters via MLE-II, and Introduction to Multiparameter Models PRML 3.5, Optional: BDA (Chapter 3), Recommended: Bayesian Inference tutorial paper slides, (print version)
Jan 23 Multiparameter Models (Contd.) Optional: BDA (Chapter 3), Recommended: Conjugate Bayesian analysis for Gaussians slides, (print version)
Jan 25 Classification: (Bayesian) Logistic Regression (and our first tryst with non-conjugacy!) MLAPP Sec 8.4, PRML Sec 4.4-4.5 slides, (print version)
Jan 30 Generative Classification, Exponential Family Distributions CS772 Lec-4 and Lec-5, MLAPP 8.6, MLAPP Sections 9.1-9.3 (exp. family) slides, (print version)
Feb 1 Gaussian Process for Learning Nonlinear Functions PRML Sec. 6.4, MLAPP Sections 15.1-15.2.5, (Optional: 15.3-15.5) slides, (print version)
Feb 6 Gaussian Process (Contd.) and Intro to Latent Variable Models Recommended: Chapter 2 and 3 of the GP book slides, (print version)
Feb 8 Inference in Latent Variable Models: The EM Algorithm PRML 9.3, 9.4 slides, (print version)
Feb 13 The EM Algorithm (Contd.) and Some Examples PRML 9.3, 9.4, 12.2 (EM for PPCA in 12.2.2). Also recommended: MLAPP Chapter 11, MLE step of GMM slides, (print version)
Feb 15 Conditional Mixture Models and Mixture of Experts PRML 14.5, MLAPP 11.2.4, 11.4.3, Recommended: Twenty Years of Mixture of Experts slides, (print version)
March 13 Probabilistic Models for Sparse Regression and Classification MLAPP 13.1, 13.2, 13.4.4, 13.7 slides, (print version)
March 15 Introduction to Variational Inference PRML 10.1, 10.2, 10.4 slides, (print version)
March 20 Variational Inference (Contd.) PRML 10.1, 10.2, 10.3, 10.4, Recommended: Variational Inference Review, Life after EM slides, (print version)
March 22 Stochastic Variational Inference Recommended: Variational Inference Review (Section 4), SVI paper slides, (print version)
March 24 Expectation Propagation and Intro to Sampling Methods PRML 10.7, 11.1 slides, (print version)
March 27 Approx. Inference via Markov Chain Monte Carlo PRML 11.2, 11.3, Recommended: Detailed Intro to MCMC slides, (print version)
April 3 Sampling (Contd.) and Gradient-based Monte Carlo Recommended: Section 3.4 of this monograph, SGLD paper, A Brief article on Hamiltonian Monte Carlo slides, (print version)
April 5 Probabilistic Models for Text and Graphs Recommended: Topic Models, MMSB paper slides, (print version)
April 7 Probabilistic Models for Sequential Data Recommended: PRML Chapter 13 (sections relevant to LDS), MLAPP Chapter 18 slides, (print version)
April 10 Nonparametric Bayesian Modeling Recommended: Overview of Nonparametric Bayesian Models slides, (print version)
April 12 Probabilistic/Bayesian Models for Deep Learning Recommended: Chapter 1 and 6 of this tutorial, Weight Uncertaintly in Neural Networks, VAE paper slides, (print version)
April 17 Bayesian Optimization Recommended: Survey on Bayesian Optimization slides, (print version)
April 19 Probabilistic Numerics, Conclusion Recommended: An Overview of Probabilistic Numerics, Other resources on probabilistic numerics slides, (print version)

Reference materials

We will primarily use lecture notes/slides from this class. In addition, we will refer to monographs and research papers for some of the topics. Some recommended, although not required, books are: