Learning a Directed Acyclic Graph in the Presence of Heteroscedastic Errors

Music City Center 

Understanding how variables causally influence each other is fundamental in many scientific fields, as it provides insights into both underlying mechanisms and the impact of interventions. In this talk, I will present a new framework for causal discovery—learning a Directed Acyclic Graph (DAG) that encodes causal relationships—when the data exhibit heteroscedastic (i.e., non-constant) error variances. I will begin by establishing conditions under which the DAG remains identifiable despite heteroscedastic noise. Building on these insights, I will introduce the ResQuE algorithm, which iteratively reconstructs the causal order and is designed to be robust against scoring misspecification, outliers, and heavy-tailed errors. I will then discuss key theoretical guarantees of ResQuE, demonstrating both structural and parameter consistency in low- and high-dimensional settings. Finally, I will showcase empirical results on synthetic and real-world causal benchmark datasets, where ResQuE compares favorably against state-of-the-art methods. I will conclude by outlining future research directions.

Graphical model