Bayesian Machine Learning
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.


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.


(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)


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:

Useful Softwares