Department of Mathematics - Mathematics Colloquium - Nonregular Causal Inference

Modern causal inference increasingly integrates flexible machine learning, optimization, and graph-based discovery methods. However, standard inferential procedures typically rely on regularity conditions—such as asymptotic normality—that often fail in realistic, data-driven, or high-dimensional settings. In this talk, we provide a unified framework for nonregular inference, where estimators deviate from classical asymptotic behavior, and we introduce practical methods for valid uncertainty quantification even under slow nuisance convergence, weak identification, or data-dependent selection. In particular, we highlight how our perturbed inference approach can restore valid coverage by injecting small perturbations that yield reliable confidence sets without requiring classical asymptotic normality. In this talk, I will focus on Perturbed Double Machine Learning and Distributionally Robust Synthetic Control.