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Orthogonal Machine Learning: Power and Limitations
Ilias Zadik · Lester Mackey · Vasilis Syrgkanis

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #11

Double machine learning provides n^{1/2}-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an n^{-1/4} rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters. We show that the n^{-1/4} requirement can be improved to n^{-1/(2k+2)} by employing a k-th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters. In the partially linear regression setting popular in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed. Our proof relies on Stein's lemma and may be of independent interest. We conclude by demonstrating the robustness benefits of an explicit doubly-orthogonal estimation procedure for treatment effect.

Author Information

Ilias Zadik (MIT)
Lester Mackey (Microsoft Research)
Vasilis Syrgkanis (Microsoft Research)

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