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Differentially Private Estimation of Heterogeneous Causal Effects

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Listed:
  • Fengshi Niu
  • Harsha Nori
  • Brian Quistorff
  • Rich Caruana
  • Donald Ngwe
  • Aadharsh Kannan

Abstract

Estimating heterogeneous treatment effects in domains such as healthcare or social science often involves sensitive data where protecting privacy is important. We introduce a general meta-algorithm for estimating conditional average treatment effects (CATE) with differential privacy (DP) guarantees. Our meta-algorithm can work with simple, single-stage CATE estimators such as S-learner and more complex multi-stage estimators such as DR and R-learner. We perform a tight privacy analysis by taking advantage of sample splitting in our meta-algorithm and the parallel composition property of differential privacy. In this paper, we implement our approach using DP-EBMs as the base learner. DP-EBMs are interpretable, high-accuracy models with privacy guarantees, which allow us to directly observe the impact of DP noise on the learned causal model. Our experiments show that multi-stage CATE estimators incur larger accuracy loss than single-stage CATE or ATE estimators and that most of the accuracy loss from differential privacy is due to an increase in variance, not biased estimates of treatment effects.

Suggested Citation

  • Fengshi Niu & Harsha Nori & Brian Quistorff & Rich Caruana & Donald Ngwe & Aadharsh Kannan, 2022. "Differentially Private Estimation of Heterogeneous Causal Effects," Papers 2202.11043, arXiv.org.
    • Handle: RePEc:arx:papers:2202.11043
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    References listed on IDEAS

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    1. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    2. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    3. Xinkun Nie & Stefan Wager, 2017. "Quasi-Oracle Estimation of Heterogeneous Treatment Effects," Papers 1712.04912, arXiv.org, revised Aug 2020.
    4. Anish Agarwal & Rahul Singh, 2021. "Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy," Papers 2107.02780, arXiv.org, revised Feb 2024.
    5. Arceneaux, Kevin & Gerber, Alan S. & Green, Donald P., 2006. "Comparing Experimental and Matching Methods Using a Large-Scale Voter Mobilization Experiment," Political Analysis, Cambridge University Press, vol. 14(1), pages 37-62, January.
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