The language of probability allows us to coherently and automatically account for uncertainty. This course will teach you how to build, fit, and do inference in probabilistic models. These models let us generate novel images and text, find meaningful latent representations of data, take advantage of large unlabeled datasets, and even let us do analogical reasoning automatically. This course will teach the basic building blocks of these models and the computational tools needed to use them.

- Lectures: Tuesdays 15:00-17:00 in SS 2117
- Tutorials: Thursday 13:00-14:00 in SS 2117
- Piazza discussion board
- Instructor: Jesse Bettencourt
- Email: csc412prof AT cs DOT toronto DOT edu - but are you sure you don't want to ask it on Piazza?
- Office hours: Wednesdays 11:30-12:30 in Bahen (BA) 2283
- Teaching assistants: Jonathan Lorraine, Reid McIlroy-Young, and Xuechen Li
- Email: csc412tas AT cs DOT toronto DOT edu - but are you sure you don't want to ask it on Piazza?

**Assignment 1:**15% (Feb 8)**Assignment 2:**15% (Mar 15)**Assignment 3:**20% (Apr ~5)**Midterm:**20% ( Feb 14)**Final:**30%

**Lecture:** Introduction (*Jan 8*)

**Tutorial:** None

**Reading:**

Murphy: Chapters 1 and 2

**Lecture:** Basic Classifiers (*Jan 16*)

**Tutorial:** Basic Supervised Learning and Probability (*Jan 17*)

**Reading:**

Murphy: Chapters 3, 4, 7-9 (excluding * sections)

**Assignment 1** Due Feb 8 at 11:59pm

LaTeX Template for Solutions and LaTeX Style File

**Lecture:** Directed Graphical Models (*Jan 22*)

**Tutorial:** Stochastic Optimization (*Jan 24*)

**Reading:**

Murphy: Chapters 10-12 (excluding * sections)

**Lecture:** Undirected Graphical Models (*Jan 29*)

**Tutorial:** Automatic Differentiation (*Jan 31*)

**Reading:**

- Murphy: Chapters 19-19.5

**Lecture:** Exact Inference (*Feb 5*)

**Tutorial:** Markov Random Fields (*Feb 7*)

**Reading:**

Murphy: Chapter 20

MacKay: Chapter 21.1 (worked example with numbers)

MacKay: Chapter 16 (Message Passing, including soldier intuition)

MacKay: Chapter 26 Exact Inference on Factor Graphs

**Assignment 1 Due** (*Feb 8*)

**Sample Midterm:** Sample Problems for the Midterm

**Lecture:** Variational Inference (*Feb 12*)

**Lecture Slides Slimmed:** Variational Inference (Thanks Trevor Ablett)

**Tutorial:** Midterm (*Feb 14*)

- Things to know for midterm:
- Bayes' rule, sum and product rules of probability, expectations
- Conditioning, normalization, marginalization
- Exponential family distributions, maximum likelihood
- Logistic regression, Naive Bayes
- Converting graphical models to pdfs and back
- Determining conditional independence
- DAGs vs UGMs vs factor graphs
- Computational complexity of inference

**Reading:**

- Murphy: Chapters 21-22

**Reading Week:** No Lecture or Tutorial

**Assignment 2** Due March 15 at 11:59pm

**Lecture:** Sampling and Monte Carlo Methods (*Feb 26*)

**Tutorial:** More on Exact Inference (*Feb 28*)

**Reading:**

MacKay Chapter 29!

**Lecture:** Sequential Data and Time-Series Models (*Mar 5*)

**Tutorial:** Gradient-based MCMC(*Mar 7*)

**Lecture Readings:**

- Murphy: Chapter 18

**Lecture:** Stochastic Variational Inference (*Mar 12*)

**Tutorial:** Gradient-based Optimization for Discrete Distributions (*Mar 14 - Slides based on Chris Maddison's Field's Talk*)

**Reading:**

**Tutorial Readings:**

Stochastic Computation Graphs

- Schulman, John, et al. "Gradient estimation using stochastic computation graphs." Advances in Neural Information Processing Systems. 2015.

Gradient Estimators

Williams, Ronald J. "Simple statistical gradient-following algorithms for connectionist reinforcement learning." Reinforcement Learning. Springer, Boston, MA, 1992. 5-32.

Kingma, Diederik P., et al. "Semi-supervised learning with deep generative models." Advances in Neural Information Processing Systems. 2014.

Maddison, Chris J., Andriy Mnih, and Yee Whye Teh. "The concrete distribution: A continuous relaxation of discrete random variables." arXiv preprint arXiv:1611.00712 (2016).

Jang, Eric, Shixiang Gu, and Ben Poole. "Categorical reparameterization with gumbel-softmax." arXiv preprint arXiv:1611.01144 (2016).

Tucker, George, et al. "REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models." Advances in Neural Information Processing Systems. 2017.

Grathwohl, Will, et al. "Backpropagation through the Void: Optimizing control variates for black-box gradient estimation." arXiv preprint arXiv:1711.00123 (2017).

Log-derivative and reparameterization tricks

**Lecture:** Variational Autoencoders (*Mar 19*)

**Tutorial:** Practicalities of SVI (*Mar 21*)

**Reading:**

**Fun Extensions**

**Lecture:** Gaussian Processes (*Mar 26*)

**Tutorial:** Expectation Maximization (*Mar 28*)

**Lecture:** Generative Adversarial Networks (*Apr 2*)

**Tutorial:** Bayesian Optimization (*Apr 4*)