CSE 515T: Bayesian Methods in Machine Learning – Fall 2019
Instructor: Professor Roman Garnett
TA: Matt Gleeson (glessonm), Adam Kern (adam.kern)
Time/Location: Monday/Wednesday 4–5:20pm, Busch 100
Office hours (Garnett): Wednesday 5:20–6:30pm, Busch 100
Piazza message board
This course will cover modern machine learning techniques from a Bayesian probabilistic perspective. Bayesian probability allows us to model and reason about all types of uncertainty. The result is a powerful, consistent framework for approaching many problems that arise in machine learning, including parameter estimation, model comparison, and decision making. We will begin with a high-level introduction to Bayesian inference, then proceed to cover more-advanced topics.
Please post questions (as a private message!) to Piazza!
You can find detailed information about the project here.
Lecture 1: Introduction to the Bayesian Method
Monday, 26 August 2019
Lecture 2: Bayesian Inference I (coin flipping)
Wednesday, 28 August 2019
Lecture 3: Bayesian Inference II (hypothesis testing and summarizing distributions)
Wednesday, 4 September 2019
- Article: "The Fallacy of Placing Confidence in Confidence Intervals" available here or here
Lecture 4: Bayesian Inference III (decision theory)
Monday, 9 September 2019
- Book: Bishop PRML: Section 1.5 (Decision theory)
- Book: Berger Chapter 1 (Basic concepts), Section 4.4 (Bayesian decision theory)
- Book: Robert Section 4.2 (Bayesian decision theory)
- Videos: YouTube user mathematicalmonk has a great series of machine-learning lectures available. Chapter 11 concerns decision theroy.
Lecture 5: The Gaussian Distribution
Wednesday, 11 September 2019
- Book: Bishop PRML: Section 2.3 (The Gaussian Distribution). This is a truly excellent and in-depth discussion!
- Book: Barber BRML: Section 8.4 (Multivariate Gaussian).
- Book/reference: Rasmussen and Williams GPML: Section A.2 (Gaussian Identities), available here. This is a good cheat sheet!
- Notes: Chuong B. Do put together some notes on the multivariate Gaussian for the Stanford machine learning class here. These go a bit more in depth than my notes, if you want to see more details.
- Website: The Wikipedia articles on the normal distribution and the multivariate normal distribution are quite complete.
- Video: YouTube user mathematicalmonk has a lecture on the multivariate normal available as well.
- Video: Alexander Ihler also has a lecture on the multivariate normal, including information on how to sample from the distribution.
Lecture 6: Bayesian Linear Regression
Monday, 16 September 2019
- Book: Bishop PRML: Section 3.3 (Bayesian Linear Regression).
- Book: Barber BRML: Section 18.1 (Regression with Additive Gaussian Noise).
- Book: Rasmussen and Williams GPML: Section 2.1 (Weight-space View), available here.
- Video: YouTube user mathematicalmonk has an entire section devoted to Bayesian linear regression. See ML 10.1–7 here.
- Videos: Nando de Freitas has a series of lectures on Bayesian linear regression. Part one is here, and part two is here.
Lecture 7: Bayesian Model Selection
Monday, 23 September 2019
- Book: Bishop PRML: Section 3.4 (Bayesian Model Comparison).
- Book: Barber BRML: Chapter 12 (Bayesian Model Selection).
- Book: MacKay ITILA: Chapter 28 (Occam's Razor and Model Comparison).
- Video: YouTube user mathematicalmonk has a lecture about Bayesian model selection (some nearby videos are related as well).
Lecture 8: Bayesian Logistic Regression / The Laplace Approximation
Wednesday, 25 September 2019
- Book: Bishop PRML: Chapter 4 (Linear Models for Classificaiton).
- Book: Barber BRML: Section 18.2 (Classification).
- Book: Rasmussen and Williams GPML: Sections 3.1 and 3.2 (Classification Problems and Linear Models for Classification), available here.
- Video: YouTube user mathematicalmonk has a lecture about Bayesian logistic regression.
Lecture 9: The Kernel Trick
Monday, 30 September 2019
- Book: Rasmussen and Williams GPML: Chapter 2 through 2.1 (Weight-space View), available here.
Lecture 10: Gaussian Process Regression
Wednesday, 2 October 2019
- Book: Rasmussen and Williams GPML: Sections 2.2 – 2.5, available here.
- Book: Barber BRML: Chapter 19 (Gaussian processes).
- Video: Nando de Freitas has a lecture here.
- Video: Philipp Hennig has a series of lectures from the 2013 Machine Learning Summer School; part one is here. The slides, which have some cool animations, are available here.
- Video: Carl Rasmussen has a two-part introduction to Gaussian processes here.
- Video: David MacKay gave an introduction to Gaussian processes here.
Lecture 11: Kernels
Monday, 6 October 2019
Lecture 12: A Quick Interlude
Wednesday, 8 October 2019
- Slides: Roman Garnett (+ Simeon Bird, Shirley Ho, and Jeff Schneider), Finding Galaxies in the Shadows of Quasars, available here.
Lecture 13: Bayesian Optimization
Wednesday, 16 October 2019
- Tutorial: Eric Brochu, Vlad M. Cora, and Nando de Freitas have a tutorial on Bayesian optimization, available here.
- Paper: Michael Osborne, Stephen J. Roberts, and I discuss the expected improvement approach to Bayesian optimization (with some tweaks/extensions) in this paper.
- Paper: Niranjan Srinivas, Andreas Krause, Sham Kakade, and Mattias Seeger discuss the GP-UCB algorithm (including theoretical results!) in this landmark paper.
- Paper: Jasper Snoek, Hugo Larochelle, and Ryan P. Adams discuss the AutoML application of Bayesian optimization here.
- Slides: Ryan P. Adams has a set of tutorial slides covering many topics available here.
Lecture 14: Bayesian Quadrature
Monday, 21 October 2019
- Slides: David Duvenaud has a set of slides introucing Bayesian quadrature, available here.
- Paper: Persi Diaconis's essay "Bayesian Numerical Analysis" from 1998 provides an excellent introduction.
- Paper: Carl Rasmussen and Zoubin Ghahramani discuss Bayesian quadrature under the name "Bayesian Monte Carlo" in this paper. Many references therein are also interesting, especially the provocatively titled Monte Carlo is fundamentally unsound by Anthony O'Hagan.
- Paper: Tom Minka wrote a report on "Deriving quadrature rules from Gaussian processes," available here.
Lecture 15: Sequential Decision Theory / Active Search
Wednesday, 23 October 2019
- Book: Berger, Sequential Decision Theory and Bayesian Analysis: Section 7.4 (Bayesian Sequential Analysis).
- Book: DeGroot, Optimal Statistical Decisions: Part 4 (Sequential Decisions).
- Paper: Garnett, et al., Bayesian Optimal Active Search and Surveying (ICML 2012).
Lecture 16: GP Classification / Assumed Density Filtering / Expectation Propagation
Wednesday, 30 October 2019
- Book: Rasmussen and Williams GPML: Chapter 3 (Classification), especially Section 3.6 (Expecation Propagation) available here.
- Book: Barber BRML: Section 28.8 (Expectation Propagation).
- Book: Bishop PRML: Section 10.7 (Expectation Propagation).
- Paper: Expectation propagation as a way of life.
Lecture 17: Practical Issues with GPs
Monday, 4 November 2019
Lecture 18: Monte Carlo, Sampling, Rejection Sampling
Wednesday, 6 November 2019
lecture slides (from Iain Murray's introduction at the 2009 Machine Learning Summer School)
- Book: Barber BRML: Section 27.1 (Sampling: Introduction).
- Book: Bishop PRML: Section 11.1 (Basic Sampling Algorithms).
- Videos: YouTube user mathematicalmonk has a chapter devoted to sampling methods (#17), beginning here.
Lecture 19: Bayesian additive regression trees (BART)
Wednesday, 13 November 2019
- Paper: The original paper is here.
There is no required book for this course. That said, there are a wide variety of machine-learning books available, some of which are available for free online. The following books all have a Bayesian slant to them:
For a more-frequentist perspective, check out the excellent The Elements of Statistical Learning by Freely available online.
- Pattern Recognition and Machine Learning (PRML) by Covers many machine-learning topics thoroughly. Definite Bayesian focus. Can also be very mathematical and take some effort to read.
- Bayesian Reasoning and Machine Learning (BRML) by Geared (as much as a machine-learning book can be!) towards computer scientists. Lots of material on graphical models. Freely available online.
- Gaussian Processes for Machine Learning (GPML) by Excellent reference for Gaussian processes. Freely available online.
- Information Theory, Inference, and Learning Algorithms by Very strong focus on information theory. If you have a background in physics or are interested in information theory, this is the book for you. Freely available online.
- I will post the source for lecture notes, demo code, etc. on this GitHub page. Even the source for the syllabus and this website are there.
- I have created a Piazza message board for this class. Please post any questions about the homework, etc. to the message board! Chances are that someone else has the same question and we can all benefit from a public discussion. If you have a question just for me and/or me and the TA, please also post this to Piazza rather than emailing us directly; you should be able to mark your message appropriately to keep it private.
- Metacademy's roadmap to Bayesian machine learning. This is a great resource for finding additional materials related to essentially every subject we will cover in this course.
- There are several relevant courses available on Coursera. Coursera gives you access to video lecture series, often from world experts, all available for free! In particular, the following three courses are all presented by leaders in the field:
The Matrix Cookbook by Kaare B. Petersen and Michael S. Pedersen can be incredibly useful for helping with tricky linear alegbra problems!