IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1901.09036.html
   My bibliography  Save this paper

Orthogonal Statistical Learning

Author

Listed:
  • Dylan J. Foster
  • Vasilis Syrgkanis

Abstract

We provide non-asymptotic excess risk guarantees for statistical learning in a setting where the population risk with respect to which we evaluate the target parameter depends on an unknown nuisance parameter that must be estimated from data. We analyze a two-stage sample splitting meta-algorithm that takes as input arbitrary estimation algorithms for the target parameter and nuisance parameter. We show that if the population risk satisfies a condition called Neyman orthogonality, the impact of the nuisance estimation error on the excess risk bound achieved by the meta-algorithm is of second order. Our theorem is agnostic to the particular algorithms used for the target and nuisance and only makes an assumption on their individual performance. This enables the use of a plethora of existing results from machine learning to give new guarantees for learning with a nuisance component. Moreover, by focusing on excess risk rather than parameter estimation, we can provide rates under weaker assumptions than in previous works and accommodate settings in which the target parameter belongs to a complex nonparametric class. We provide conditions on the metric entropy of the nuisance and target classes such that oracle rates of the same order as if we knew the nuisance parameter are achieved.

Suggested Citation

  • Dylan J. Foster & Vasilis Syrgkanis, 2019. "Orthogonal Statistical Learning," Papers 1901.09036, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:1901.09036
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1901.09036
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yingqi Zhao & Donglin Zeng & A. John Rush & Michael R. Kosorok, 2012. "Estimating Individualized Treatment Rules Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1106-1118, September.
    2. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Lester Mackey & Vasilis Syrgkanis & Ilias Zadik, 2017. "Orthogonal Machine Learning: Power and Limitations," Papers 1711.00342, arXiv.org, revised Aug 2018.
    5. Miruna Oprescu & Vasilis Syrgkanis & Zhiwei Steven Wu, 2018. "Orthogonal Random Forest for Causal Inference," Papers 1806.03467, arXiv.org, revised Sep 2019.
    6. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    7. Xin Zhou & Nicole Mayer-Hamblett & Umer Khan & Michael R. Kosorok, 2017. "Residual Weighted Learning for Estimating Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 169-187, January.
    8. Denis Nekipelov & Vira Semenova & Vasilis Syrgkanis, 2018. "Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models," Papers 1806.04823, arXiv.org, revised Sep 2021.
    9. Athey, Susan & Wager, Stefan, 2017. "Efficient Policy Learning," Research Papers 3506, Stanford University, Graduate School of Business.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jikai Jin & Vasilis Syrgkanis, 2024. "Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation," Papers 2402.14264, arXiv.org, revised Mar 2024.
    2. Nora Bearth & Michael Lechner, 2024. "Causal Machine Learning for Moderation Effects," Papers 2401.08290, arXiv.org, revised Apr 2024.
    3. Stefan Wager, 2024. "Sequential Validation of Treatment Heterogeneity," Papers 2405.05534, arXiv.org.
    4. Jacob Dorn & Kevin Guo & Nathan Kallus, 2021. "Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding," Papers 2112.11449, arXiv.org, revised Jul 2022.
    5. Ruohan Zhan & Shichao Han & Yuchen Hu & Zhenling Jiang, 2024. "Estimating Treatment Effects under Recommender Interference: A Structured Neural Networks Approach," Papers 2406.14380, arXiv.org, revised Jul 2024.
    6. Michael Lechner & Jana Mareckova, 2024. "Comprehensive Causal Machine Learning," Papers 2405.10198, arXiv.org.
    7. Hui Lan & Vasilis Syrgkanis, 2023. "Causal Q-Aggregation for CATE Model Selection," Papers 2310.16945, arXiv.org, revised Nov 2023.
    8. Retsef Levi & Elisabeth Paulson & Georgia Perakis & Emily Zhang, 2024. "Heterogeneous Treatment Effects in Panel Data," Papers 2406.05633, arXiv.org.
    9. David M. Ritzwoller & Vasilis Syrgkanis, 2024. "Simultaneous Inference for Local Structural Parameters with Random Forests," Papers 2405.07860, arXiv.org, revised Sep 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mert Demirer & Vasilis Syrgkanis & Greg Lewis & Victor Chernozhukov, 2019. "Semi-Parametric Efficient Policy Learning with Continuous Actions," CeMMAP working papers CWP34/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.
    4. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    5. Daniel Jacob, 2021. "CATE meets ML -- The Conditional Average Treatment Effect and Machine Learning," Papers 2104.09935, arXiv.org, revised Apr 2021.
    6. Daniel Jacob, 2021. "CATE meets ML," Digital Finance, Springer, vol. 3(2), pages 99-148, June.
    7. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    8. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Crystal T. Nguyen & Daniel J. Luckett & Anna R. Kahkoska & Grace E. Shearrer & Donna Spruijt‐Metz & Jaimie N. Davis & Michael R. Kosorok, 2020. "Estimating individualized treatment regimes from crossover designs," Biometrics, The International Biometric Society, vol. 76(3), pages 778-788, September.
    10. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    11. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    12. Andrew Bennett & Nathan Kallus, 2020. "Efficient Policy Learning from Surrogate-Loss Classification Reductions," Papers 2002.05153, arXiv.org.
    13. Khashayar Khosravi & Greg Lewis & Vasilis Syrgkanis, 2019. "Non-Parametric Inference Adaptive to Intrinsic Dimension," Papers 1901.03719, arXiv.org, revised Jun 2019.
    14. Yunan Wu & Lan Wang, 2021. "Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes," Biometrics, The International Biometric Society, vol. 77(2), pages 465-476, June.
    15. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    16. Jikai Jin & Vasilis Syrgkanis, 2024. "Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation," Papers 2402.14264, arXiv.org, revised Mar 2024.
    17. Ravi Kumar & Shahin Boluki & Karl Isler & Jonas Rauch & Darius Walczak, 2022. "Machine Learning based Framework for Robust Price-Sensitivity Estimation with Application to Airline Pricing," Papers 2205.01875, arXiv.org, revised Dec 2022.
    18. Jacob, Daniel, 2020. "Cross-Fitting and Averaging for Machine Learning Estimation of Heterogeneous Treatment Effects," IRTG 1792 Discussion Papers 2020-014, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    19. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for a Continuous Treatment," Papers 2402.02535, arXiv.org.
    20. Q. Clairon & R. Henderson & N. J. Young & E. D. Wilson & C. J. Taylor, 2021. "Adaptive treatment and robust control," Biometrics, The International Biometric Society, vol. 77(1), pages 223-236, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1901.09036. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.