Source Condition Double Robust Inference on Functionals of Inverse Problems

Abstract:

We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source condition double robust inference method that ensures asymptotic normality around the parameter of interest as long as either the primal or the dual inverse problem is sufficiently well-posed, without knowledge of which inverse problem is the more well-posed one. Our result is enabled by novel guarantees for iterated Tikhonov regularized adversarial estimators for linear inverse problems, over general hypothesis spaces, which are developments of independent interest.

Paper: arxiv.org/pdf/2307.13793.pdf

Bio:

Vasilis Syrgkanis is an Assistant Professor of Management Science and Engineering and (by courtesy) of Computer Science and Electrical Engineering at Stanford University. Prior to that he was a Principal Researcher at Microsoft Research, New England, where he was co-leading the project on Automated Learning and Intelligence for Causation and Economics (ALICE). He received his Ph.D. in Computer Science from Cornell University in 2014, under the supervision of Prof. Eva Tardos and spent two years at Microsoft Research, New York as a postdoctoral researcher. His research addresses problems at the intersection of machine learning, causal inference, economics, statistics and theoretical computer science. His work has received several awards, such as best paper awards at the 2015 ACM Conference on Economics and Computation (EC’15), the 2015 Annual Conference on Neural Information Processing Systems (NeurIPS’15) and the Conference on Learning Theory (COLT’19),  the Bodossaki Distinguished Young Scientist award and an Amazon Research award.