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Double/de-biased machine learning using regularized Riesz representers

Author

Listed:
  • Victor Chernozhukov

    (Institute for Fiscal Studies and MIT)

  • Whitney K. Newey

    (Institute for Fiscal Studies and MIT)

  • James Robins

    (Institute for Fiscal Studies)

Abstract

We provide adaptive inference methods for linear functionals of L1-regularized linear approximations to the conditional expectation function. Examples of such functionals include average derivatives, policy effects, average treatment effects, and many others. The construction relies on building Neyman-orthogonal equations that are approximately invariant to perturbations of the nuisance parameters, including the Riesz representer for the linear functionals. We use L1-regularized methods to learn the approximations to the regression function and the Riesz representer, and construct the estimator for the linear functionals as the solution to the orthogonal estimating equations. We establish that under weak assumptions the estimator concentrates in a 1/vn neighborhood of the target with deviations controlled by the normal laws, and the estimator attains the semi-parametric efficiency bound in many cases. In particular, either the approximation to the regression function or the approximation to the Rietz representer can be “dense” as long as one of them is sufficiently “sparse”. Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models.

Suggested Citation

  • Victor Chernozhukov & Whitney K. Newey & James Robins, 2018. "Double/de-biased machine learning using regularized Riesz representers," CeMMAP working papers CWP15/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:15/18
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    References listed on IDEAS

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    1. Yinchu Zhu & Jelena Bradic, 2018. "Linear Hypothesis Testing in Dense High-Dimensional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1583-1600, October.
    2. 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.
    3. A. Belloni & V. Chernozhukov & K. Kato, 2015. "Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems," Biometrika, Biometrika Trust, vol. 102(1), pages 77-94.
    4. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 649-688, August.
    5. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform post selection inference for LAD regression models," CeMMAP working papers CWP24/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    7. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    8. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    Citations

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    Cited by:

    1. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. 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.
    3. Adel Daoud, 2021. "The International Monetary Funds intervention in education systems and its impact on childrens chances of completing school," Papers 2201.00013, arXiv.org.
    4. Daoud, Adel & Johansson, Fredrik, 2019. "Estimating Treatment Heterogeneity of International Monetary Fund Programs on Child Poverty with Generalized Random Forest," SocArXiv awfjt, Center for Open Science.
    5. 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.
    6. Victor Chernozhukov & Jerry Hausman & Whitney K. Newey, 2019. "Demand analysis with many prices," CeMMAP working papers CWP59/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Daoud, Adel, 2021. "The International Monetary Fund’s intervention in education systems and its impact on children’s chances of completing school," SocArXiv kbc34, Center for Open Science.
    8. Jann Spiess & Vasilis Syrgkanis & Victor Yaneng Wang, 2021. "Finding Subgroups with Significant Treatment Effects," Papers 2103.07066, arXiv.org, revised Dec 2023.

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    More about this item

    Keywords

    Approximate Sparsity vs. Density; Double/De-biased Machine Learning; Regularized Riesz Representers; Linear Functionals;
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