Orthogonal Machine Learning: Power and Limitations

Lester Mackey, Vasilis Syrgkanis, Ilias Zadik
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:3375-3383, 2018.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-mackey18a, title = {Orthogonal Machine Learning: Power and Limitations}, author = {Mackey, Lester and Syrgkanis, Vasilis and Zadik, Ilias}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3375--3383}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/mackey18a/mackey18a.pdf}, url = {https://proceedings.mlr.press/v80/mackey18a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Orthogonal Machine Learning: Power and Limitations %A Lester Mackey %A Vasilis Syrgkanis %A Ilias Zadik %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-mackey18a %I PMLR %P 3375--3383 %U https://proceedings.mlr.press/v80/mackey18a.html %V 80 %X 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.
APA
Mackey, L., Syrgkanis, V. & Zadik, I.. (2018). Orthogonal Machine Learning: Power and Limitations. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:3375-3383 Available from https://proceedings.mlr.press/v80/mackey18a.html.

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