## Center for Applied Mathematics Colloquium

Abstract: Causal discovery procedures are popular methods for discovering causal structure across the physical, biological, and social sciences. However, most procedures for causal discovery only output a single estimated causal model or single equivalence class of models. In this work, we propose a procedure for quantifying uncertainty in causal discovery. Specifically, we consider structural equation models where a unique graph can be identified and propose a procedure which returns a confidence sets of causal orderings which are not ruled out by the data. We show that asymptotically, a true causal ordering will be contained in the returned set with some user specified probability. In addition, the confidence set can be used to form conservative sets of ancestral relationships.

Bio: Sam Wang is currently an assistant professor at Cornell in the Department of Statistics and Data Science. He was previously a post-doc at the University of Chicago and completed his PhD in Statistics at the University of Washington. Sam enjoys thinking about problems where the goal is to discover interpretable structure which underlies the data generating process. This includes problems in the areas of causal discovery, graphical models, and mixed membership models. In many cases, the methods are tailored for the high-dimensional setting where the number of variables considered may be large when compared to the number of observed samples. His applied interests vary but are generally social science related.