CS798D: Algorithms for Bayesian Networks and Causality

CS798D: Algorithms for Bayesian Networks and Causality

Prerequisites: Basics of statistics and probability.

Short description:

• Probabilistic graphical models (PGM): In the first part of the course, we will discuss how to model dependent random variables using graphs. In general, computational problems about the joint distribution on such variables quickly becomes intractable as the number of dimensions grow. However, in many natural scenarios the random variables for each dimension are interdependent in a limited manner. A PGM encodes such a dependence using graphical concepts and hence allows us to define such a joint distribution.
• Discrete and Gaussian Bayesian network: In this part, we will discuss how to learn the underlying graph of a PGM given independent samples from it. Of specific interest will be Bayesian networks, where the underlying graph is a directed acyclic graph of small indegree. The random variables involved could be discrete or continuous. Bayesian networks have turned out to be immensely useful in modelling several practical mechanisms such as gene regulatory networks.  We will derive sample complexity bounds for learning a Bayesian network. Finally, we will likely take a detour of Gaussian graphical models if the time permits.
• Causality: In this part, we will start by discussing Judea Pearl's graphical approach of modelling causality using Bayesian networks. We will introduce interventions and discuss identification of causal effects from observational data. We will then discuss the important problem of learning causal structures from observational data and disucss several algorithms such as FCI and LiNGAM which have been successful in practice.
• In the final part of the course we will read important classical and recent literature on Bayesian networks and causality; and discuss how causal inference techniques have been successful in practical fields such as machine learning.

References and resources:

• Probabilistic Graphical Models by Daphne Koller and Nir Friedman
• Causality by Judea Pearl
• Dissertation of Prof. Jin Tian (Ph.D. UCLA, currently at Iowa State)
• The Simons Institute is currently hosting a program on Causality. Video lectures are available from their webpage.