Bayesian Machine Learning
CS698S
2016-17 (even semester)

Instructor: Piyush Rai: (office: KD-319, email: piyush AT cse DOT iitk DOT ac DOT in)
Class Venue: KD-101
Class Timings: MW 5:10-6:25pm
Instructor Office Hours: Thursday 4-5pm (KD-319)
TAs: Vijay Pal (vjpal@cse), Utsav Singh (utsavz@cse), Munender Kumar (munenderv@cse), Vinay Verma (vkverma@cse)
TA Office Hours: Vijay (Mon 4-5pm, KD-305), Munender (Tue 4-5pm, RM-504), Utsav (Wed 4-5pm, KD-315), Vinay (Fri 4-5pm, RM-504)
Q/A Forum: Piazza

Background and Course Description

This course will take the Bayesian statistical modeling approach to machine learning. Some of the key benefits of the Bayesian approach include the ability to quantify the uncertainty in the parameters/predictions through posterior probability distributions, the ability to incorporate prior knowledge in a principled way, the ability to learn the model hyperparameters and the right model size/complexity automatically from data, and the property of embodying online learning in a natural way. In this course, we will discuss the foundations of Bayesian modeling, especially in the context of machine learning and, through various case-studies/running-examples, we will look at how to set up a machine learning problem as a Bayesian model and how to design sampling/optimization techniques to perform computationally scalable inference in these models.

Pre-requisites

Instructor's consent. However, note that this course will make extensive use of concepts from probability, statistics, and optimization. Therefore a solid background on these topics, as well as introductory machine learning, will be essential. Students are also supposed to be familiar with programming in MATLAB/Python.

Grading

(Tentative break-up) There will be 4 homework assignments (total 25%) which may include a programming component, a mid-term (20%), a final-exam (25%), and a course project (25%). Class/Piazza participation will be worth 5% of your total grade.

Schedule (Tentative)

Date	Topics	Readings/References	Slides/Notes
Jan 9	Course Logistics and Introduction to Bayesian Machine Learning	Nature article, A Roadmap to Bayesian ML	slides (print version)
Jan 11	A Warm-up via Simple Models: Beta-Bernoulli Model and Bayesian Linear Regression	Probability tutorial slides. PRML (Bishop) Chapter 2 (+ appendix B), or MLAPP (Murphy) Chapter 2, Wikipedia Entry on Conjugate Priors	slides (print version)
Jan 16	Bayesian Inference with Gaussian Distributions, Bayesian Linear Regression (revisited)	PRML (Bishop) Section 2.3 (up to 2.3.6), Section 3.3 (up to 3.3.2). Optional: MLAPP (Murphy) Chapter 4	slides (print version)
Jan 18	Bayesian Generative Classification, and Bayesian naïve Bayes	Optional: MLAPP (Murphy) Section 3.5	slides (print version)
Jan 23	Bayesian Discriminative Classification (Bayesian Logistic Regression). Inference via Laplace Approximation	MLAPP (Murphy) Section 8.4 (optional: Section 8.1-8.3 for background on Logistic Regression)	slides (print version)
Jan 25	Exponential Family and Its Role in Probabilistic Inference	PRML (Bishop) Section 2.4, or MLAPP (Murphy) Section 9.1-9.2	slides (print version)
Jan 30	Exponential Family (Contd.)	MLAPP (Murphy) Section 9.1-9.2	slides (print version)
Feb 1	Generalized Linear Models and Their Applications	MLAPP (Murphy) Section 9.3	slides (print version)
Feb 6	Bayesian Inference with (Point) Estimation of Hyperparameters	Optional: Mike Tipping's tutorial paper on Bayesian Inference	slides (print version)
Feb 11	Bayesian Inference with Local Conjugacy	Optional Reading: Paper on Bayesian Probabilistic Matrix Factorization	slides (print version)
Feb 13	Approximate Bayesian Inference: Sampling Methods (1)	MLAPP (Murphy) Section 23.1-23.4.2, Optional: Intro to MCMC (up to Section 2)	slides (print version)
Feb 15	Approximate Bayesian Inference: Sampling Methods (2)	MLAPP (Murphy Section 24.1-24.3	slides (print version)
Feb 20	Approximate Bayesian Inference: Variational Bayes (1)	PRML (Bishop) Section 10.1.1 and 10.1.3. Recommended: Variational Inference: A Review for Statisticians	slides (print version)
Feb 22	Approximate Bayesian Inference: Variational Bayes (2)	PRML (Bishop) Section 10.1 - 10.4. Recommended: Variational Inference: A Review for Statisticians	slides (print version)
Mar 6	Approximate Bayesian Inference: Scalable Inference via Stochastic VB	Optional Reading: Section 5.1-5.2 of this monograph	slides (print version)
Mar 8	Approximate Bayesian Inference: Some Other Methods (EP, SGLD - MCMC using Gradients, ABC)	PRML (Bishop) Section 10.7 and 10.7.1 for EP, Optional: SGLD paper, Another paper, Wikipedia Article on ABC	slides (print version)
Mar 20	Bayesian Nonparametrics: Gaussian Process for Nonparametric Function Approximation	MLAPP (Murphy) Sections 15.1-15.2.5, (Optional: 15.3-15.5)	slides (print version)
Mar 22	Bayesian Nonparametrics: Dirichlet Process for Nonparametric Bayesian Clustering	MLAPP (Murphy) Section 25.2	slides (print version)
Mar 27	Bayesian Nonparametrics: Dirichlet Process Properties, Extensions, Beta Process	MLAPP (Murphy) Section 25.2, Optional: Dirichlet Process, A good informal description of DP with some demos	slides, (print version)
Mar 29	Bayesian Topic Models: Latent Dirichlet Allocation and Extensions	Optional Readings: Intro to Topic Models, Probabilistic Topic Models	slides, (print version)
Apr 3	Bayesian Deep Learning: Deep Latent Gaussian Models and Variational Autoencoders	On Bayesian Deep Learning, VAE: A Tutorial, Another Tutorial: Part 1, Part 2, An intuitive explanation of VAEs	slides, (print version)
Apr 5	Bayesian Deep Learning: Variational Autoencoders (Contd.), and Other Deep Generative Models	Readings from lecture 21 + Some optional readings: VAE paper, Structured VAE paper, Deep Exponential Families, Deep GPs	slides, (print version)
Apr 10	Bayesian Optimization	Optional Reading: Survey on Bayesian Optimization	slides, (print version)
Apr 12	Bayesian State-Space Models and Kalman Filtering	Optional Reading: Unified Overview of Linear Gaussian Models	slides, (print version)
Apr 17	Probabilistic Numerics and Bayesian Quadrature	Optional Reading: An Overview of Probabilistic Numerics, Other resources on probabilistic numerics	slides, (print version)
Apr 19	Perspectives on Bayesian Machine Learning	Additional slides from the Review class	slides, (print version)

Books

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

Christopher Bishop, Pattern Recognition and Machine Learning (PRML), Springer, 2007.
Kevin Murphy, Machine Learning: A Probabilistic Perspective (MLAPP), MIT Press, 2012
Carl Rasmussen and Chris Williams. Gaussian Processes for Machine Learning. The MIT Press, 2006.
David Mackay. Information Theory, Inference, and Learning Algorithms. Cambridge Univ. Press, 2003.
David Barber. Bayesian Reasoning and Machine Learning Cambridge Univ. Press, 2012.
Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin. Bayesian Data Analysis, Chapman & Hall/CRC, 2013.

Useful Softwares

MATLAB software accompanying the MLAPP book. Contains code and demos for most of the algorithms in the book.
Edward: Python Library for Probabilistic Modeling and Inference. Highly recommended: very useful for quick prototyping of probabilistic models and building new models. Some documentation can be found here and here .

Stan Probabilistic Programming Language. Highly recommended: very useful for quick prototyping of probabilistic models and building new models. Some documentation can be found here.
BNPy: Bayesian nonparametric machine learning in Python
GPML (MATLAB based) and GPStuff (MATLAB/Octave/R based): Libraries for developing Gaussian Process (GP) based models, which allow learning nonlinear functions in a fully Bayesian way.
Infer.NET: A framework (from Microsoft) for doing Bayesian inference in probabilistic graphical models

Bayesian Machine Learning CS698S 2016-17 (even semester)