CSE 515T: Bayesian Methods in Machine Learning – Fall 2019

Lecture 1: Introduction to the Bayesian Method

Additional Resources:

• Book: Bishop PRML: Section 1.2 (Probability theory)
• Book: Barber BRML: Chapter 1 (Probabilistic reasoning)
• Video: Bayesian Method for Hackers (Cam Davidson Pilon) Great high-level overview from an atypical perspective!
• Video: Introduction to Machine Learning (Nando de Freitas)
• Video: Bayesian Inference I (Zoubin Ghahramani) (the first 30 minutes or so)
• Video: Machine Learning Coursera course (Andrew Ng) The first week gives a good general overview of machine learning and the third week provides a linear-algebra refresher.

Lecture 2: Bayesian Inference I (coin flipping)

Additional Resources:

• Book: Bishop PRML: Section 2.1 (Binary variables)
• Website: Wikipedia has an article on checking whether a coin is fair.
• Website: Marcus Brinkmann (lambdafu) has put together a Python notebook on Bayesian coin flipping.

Lecture 3: Bayesian Inference II (hypothesis testing and summarizing distributions)

Additional Resources:

• Article: "The Fallacy of Placing Confidence in Confidence Intervals" available here or here

Lecture 4: Bayesian Inference III (decision theory)

Additional Resources:

• 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

Additional Resources:

• 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

Additional Resources:

• 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

Additional Resources:

• 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

Additional Resources:

• 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

Additional Resources:

• Book: Rasmussen and Williams GPML: Chapter 2 through 2.1 (Weight-space View), available here.

Lecture 10: Gaussian Process Regression

Additional Resources/Notes:

• 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

Resources/Notes:

• Book: Bishop PRML: Chapter 6 (Kernel Methods).
• Book: Barber BRML: Section 19.3 (Covariance Functions).
• Book: Rasmussen and Williams GPML: Chapter 4 (Covariance Functions), available here.
• Website: David Duvenaud has made a "kernel cookbook," available here. This webpage also became a chapter of his thesis.
• Website: Metacademy has a pages on the kernel trick and constructing kernels.

Lecture 12: A Quick Interlude

Additional Resources/Notes:

• Slides: Roman Garnett (+ Simeon Bird, Shirley Ho, and Jeff Schneider), Finding Galaxies in the Shadows of Quasars, available here.

Lecture 13: Bayesian Optimization

Additional Resources/Notes:

• 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

Additional Resources/Notes:

• 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

Additional Resources/Notes:

• 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

Additional Resources/Notes:

• 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

Lecture 18: Monte Carlo, Sampling, Rejection Sampling

• 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)

Additional Resources/Notes:

• Paper: The original paper is here.

Books

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:

• Pattern Recognition and Machine Learning (PRML) by Christopher M. Bishop. 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 David Barber. 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 Carl Rasmussen and Christopher Williams. Excellent reference for Gaussian processes. Freely available online.
• Information Theory, Inference, and Learning Algorithms by David J. C. Mackay. 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.