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Orthogonal Machine Learning: Power and Limitations

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  • Lester Mackey
  • Vasilis Syrgkanis
  • Ilias Zadik

Abstract

Double machine learning provides $\sqrt{n}$-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.

Suggested Citation

  • Lester Mackey & Vasilis Syrgkanis & Ilias Zadik, 2017. "Orthogonal Machine Learning: Power and Limitations," Papers 1711.00342, arXiv.org, revised Aug 2018.
  • Handle: RePEc:arx:papers:1711.00342
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers CWP49/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    Cited by:

    1. Dylan J. Foster & Vasilis Syrgkanis, 2019. "Orthogonal Statistical Learning," Papers 1901.09036, arXiv.org, revised Sep 2020.
    2. Yiyan Huang & Cheuk Hang Leung & Xing Yan & Qi Wu & Nanbo Peng & Dongdong Wang & Zhixiang Huang, 2020. "The Causal Learning of Retail Delinquency," Papers 2012.09448, arXiv.org.
    3. Jelena Bradic & Victor Chernozhukov & Whitney K. Newey & Yinchu Zhu, 2019. "Minimax Semiparametric Learning With Approximate Sparsity," Papers 1912.12213, arXiv.org.
    4. Khashayar Khosravi & Greg Lewis & Vasilis Syrgkanis, 2019. "Non-Parametric Inference Adaptive to Intrinsic Dimension," Papers 1901.03719, arXiv.org, revised Jun 2019.
    5. Krikamol Muandet & Wittawat Jitkrittum & Jonas Kubler, 2020. "Kernel Conditional Moment Test via Maximum Moment Restriction," Papers 2002.09225, arXiv.org, revised Jun 2020.
    6. Sookyo Jeong & Hongseok Namkoong, 2020. "Robust Causal Inference Under Covariate Shift via Worst-Case Subpopulation Treatment Effects," Papers 2007.02411, arXiv.org, revised Jul 2020.

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