## MATH 605D Open to All

This fall, MATH 605D: Graphical Models and Causal Discovery will be open to everyone (please note the prerequisites).

**Class time: **Tuesday and Thursday 11 AM -12:30 PM (the time and day might change if needed)

**Location: **MATH 225

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

**Course description:** This research-oriented course will explore the theoretical underpinnings of graphical modeling and causality. Graphical models are commonly used in machine learning to depict complex dependence structures 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 directly 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.