## Statistics Seminar

I will present recent advances in using modern optimization and representation learning for learning causal effects and causal-effect-maximizing policies from observational data. Central to these is a new, encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference called generalized optimal matching (GOM). The framework is given by generalizing a new functional-analytical formulation of classic optimal matching, giving rise to the class of GOM methods, for which I provide a single unified theory to analyze tractability, consistency, and efficiency. Many commonly used existing methods are included in GOM and, using their GOM interpretation, can be extended to optimally and automatically trade off balance for variance and outperform their standard counterparts. As a subclass, GOM gives rise to kernel optimal matching (KOM), which, as supported by new theory, I will show is notable for combining the interpretability of matching methods, the non-parametric model-free consistency of optimal matching, the efficiency of well-specified regression, the efficiency and robustness of augmented inverse propensity weight estimators, the judicious sample size selection of monotonic imbalance bounding methods, and the model-selection flexibility of Gaussian-process regression. New inference methods for KOM enable partial (interval) identification of causal effects even in the absence of necessary overlap conditions.

The GOM approach is particularly apt for the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes, where only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising, where existing approaches rely on fragile and inefficient plug-in approaches leading to high-variance evaluation and ineffective learning. I will present a new GOM-based policy learner that proceeds as a bilevel optimization problem and demonstrably outperforms existing approaches both in evaluation and learning, as supported by new regret bounds for the method. I will conclude by discussing exciting new directions for balancing as a new paradigm for causal inference methods in other settings as well as new applications and challenges for policy learning from observational data.