## Math 605D Graphical Models and Causal Discovery

### Elina Robeva, The University of British Columbia, Winter Term 1 2024

## Course Information

Class time: TTh 11:00am - 12:30pm Pacific Time; September 5 - December 5, 2024

Location: Math 225

Mailing list: Fill out this form to receive class emails

Instructor: Elina Robeva; erobeva@math.ubc.ca

Prerequisites: Linear algebra (e.g., one of Math 221, 223, 307), Probability theory (e.g., one of Math 302, 318)

Grading: Final project: 50%; Homework: 40%; Attendance and participation: 10%.

Office hours: Tuesdays 12:30pm - 1:20pm in MATX 1106.

## Overview

This research-oriented course will explore the theoretical underpinnings of graphical modeling and causality. A graphical model is a mathematical structure that describes complex dependencies between random variables. More precisely, given a (directed or undirected) graph, we envision one random variable at each vertex. The graphical structure gives rise to conditional independence statements and, in the directed case, to functional relationships among the variables. Given data from a graphical model, we will discuss model selection: the problem of finding the graph that the data arose from, and inference: the problem of estimating the distribution assuming we know the graph. We will explore different types of algorithms used to solve these questions as well as the mathematical theory involved.

Building on the theory of graphical models, we will study causal discovery. Here, we are interested in finding a directed graph that depicts the causal relationships among the observed random variables (e.g., X --> Y if X causes Y). We will discuss how to solve this problem in both the observational and interventional (e.g. randomized control trials) settings. We will conclude with theory and algorithms for the case of hidden variables as well as directed cycles in the graph.