Orthogonal Machine Learning: Power and Limitations
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:33753383, 2018.
Abstract
Double machine learning provides n^{1/2}consistent estimates of parameters of interest even when highdimensional or nonparametric nuisance parameters are estimated at an n^{1/4} rate. The key is to employ Neymanorthogonal moment equations which are firstorder 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 kth order notion of orthogonality that grants robustness to more complex or higherdimensional nuisance parameters. In the partially linear regression setting popular in causal inference, we show that we can construct secondorder 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 doublyorthogonal estimation procedure for treatment effect.
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