Course Graphical Models (COMPSCI 688, Spring 2021)

Time Tuesday + Thursday / 4:00PM-5:15PM

Course Final: Day 4 at 4:30pm (see Final Exam Matrix)

Course Description Probabilistic graphical models are an intuitive visual language for describing the structure of joint probability distributions using graphs. They enable the compact representation and manipulation of exponentially large probability distributions, which allows them to efficiently manage the uncertainty and partial observability that commonly occur in real-world problems. As a result, graphical models have become invaluable tools in a wide range of areas from computer vision and sensor networks to natural language processing and computational biology. The aim of this course is to develop the knowledge and skills necessary to effectively design, implement and apply these models to solve real problems. The course will cover (a) Bayesian and Markov networks and their dynamic and relational extensions; (b) exact and approximate inference methods; (c) estimation of both the parameters and structure of graphical models. Although the course is listed as a seminar, it will be taught as a regular lecture course with programming assignments and exams. Students entering the class should have good programming skills and knowledge of algorithms. Undergraduate-level knowledge of probability and statistics is recommended.

Textbook (none) We will distribute lecture notes as well as some readings from papers and online resources.

Prerequisites I will assume a strong working knowledge of linear algebra, probability theory, programming ability in some language, and that you have some familiarity with basic machine learning methods.

• Probability Theory
• Linear Algebra and Matrix Calculus
• Matrix Cookbook
• Matrix Identitites

Topics

• Directed Models
• Bayes Ball
• D-separation
• Maximum Likelihood in Discrete Directed Models
• Exact inference via Message-Passing
• Exponential families and maximum likelihood