Instructor: Professor Roman Garnett

TA: Yehu Chen

Time/Location: Monday/Wednesday 10–11:20am, Seigle 301

Office hours (Garnett): by appointment, always on Slack

syllabus

Slack invite link

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.

You can find detailed information about the project here.

Please post questions to Slack!

Assignment 1, due **18 September 2024.**

Assignment 2, due **2 October 2024.**

lecture notes

Additional Resources:

- Book: Bishop PRML: Section 1.2 (Probability theory)
- Book: Barber BRML: Chapter 1 (Probabilistic reasoning)
- Book: Garnett BayesOpt: Section 1.2 (The Bayesian Approach)
- Book: 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 notes

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 notes &ndsh; see Garnett BayesOpt: Appendix A

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!
- 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 notes

Additional Resources:

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

lecture notes

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 notes

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 notes

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).
- Book: Garnett BayesOpt: Chapter 4 (Model Assessment, Selection, and Averaging).
- Video: YouTube user mathematicalmonk has a lecture about Bayesian model selection (some nearby videos are related as well).

lecture notes

Additional Resources:

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

lecture notes

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.

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 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.*Bayesian optimization*by Although the focus is on Bayesian optimization, there is a lot of background material on Gaussian processes as well. 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 Slack for this class (invite link). Please post any questions about lectures, homework, etc here! 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 send a direct message via Slack rather than emailing us directly.
- 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:
- Andrew Ng's Machine Learning course (Stanford University)
- Daphne Koller's Probabilistic Graphical Models course (Stanford University)

The Matrix Cookbook by Kaare B. Petersen and Michael S. Pedersen can be incredibly useful for helping with tricky linear alegbra problems!