Primary Submission Category: Instrumental Variables
Source Condition Double Robust Inference on Functionals of Inverse Problems
Authors: Vasilis Syrgkanis, Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Masatoshi Uehara,
Presenting Author: Vasilis Syrgkanis*
We consider estimation of parameters defined as linear functionals of solutions to linear inverse prob- lems. 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 estima- tors for linear inverse problems, over general hypothesis spaces, which are developments of independent interest.