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Distributional conformal prediction

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  • Chernozhukov, Victor
  • Wüthrich, Kaspar
  • Zhu, Yinchu

Abstract

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems, including cross-sectional prediction, k -step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, under overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.

Suggested Citation

  • Chernozhukov, Victor & Wüthrich, Kaspar & Zhu, Yinchu, 2021. "Distributional conformal prediction," University of California at San Diego, Economics Working Paper Series qt2zs6m5p5, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt2zs6m5p5
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
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    22. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2018. "Exact and robust conformal inference methods for predictive machine learning with dependent data," CeMMAP working papers CWP16/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    1. Interval Prediction
      by Francis Diebold in No Hesitations on 2019-10-12 19:16:00

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    Cited by:

    1. Leying Guan, 2023. "Localized conformal prediction: a generalized inference framework for conformal prediction," Biometrika, Biometrika Trust, vol. 110(1), pages 33-50.

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    More about this item

    Keywords

    prediction intervals; conditional validity; model-free validity; quantile regression; distribution regression;
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