Distribution-Free Predictive Inference for Regression

We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preser...

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Published in:	Journal of the American Statistical Association Vol. 113; no. 523; pp. 1094 - 1111
Main Authors:	Lei, Jing, G'Sell, Max, Rinaldo, Alessandro, Tibshirani, Ryan J., Wasserman, Larry
Format:	Journal Article
Language:	English
Published:	Alexandria Taylor & Francis 03.07.2018 Taylor & Francis Group,LLC Taylor & Francis Ltd
Subjects:	Computational efficiency computer software Computing time Distribution-free Empirical analysis equations heteroskedasticity Inference Intervals Model misspecification prediction Prediction band Predictions Property Regression Regression analysis Reproducibility Statistical analysis Statistical methods Statistics Theory and Methods Variable importance Variants
ISSN:	0162-1459, 1537-274X, 1537-274X
Online Access:	Get full text
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Abstract	We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, to adapt to heteroscedasticity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this article is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.
AbstractList	We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, to adapt to heteroscedasticity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this article is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package. We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformal framework: full conformal inference and split conformal inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformal inference, which has essentially the same computational efficiency as split conformal inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, to adapt to heteroscedasticity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this article is an R package conformalInference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package. We develop a general framework for distribution-free predictive inference in regression, using conformai inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency properties of the original estimator under standard assumptions, while guaranteeing finite-sample marginal coverage even when these assumptions do not hold. We analyze and compare, both empirically and theoretically, the two major variants of our conformai framework: full conformai inference and split conformai inference, along with a related jackknife method. These methods offer different tradeoffs between statistical accuracy (length of resulting prediction intervals) and computational efficiency. As extensions, we develop a method for constructing valid in-sample prediction intervals called rank-one-out conformai inference, which has essentially the same computational efficiency as split conformai inference. We also describe an extension of our procedures for producing prediction bands with locally varying length, to adapt to heteroscedasticity in the data. Finally, we propose a model-free notion of variable importance, called leave-one-covariate-out or LOCO inference. Accompanying this article is an R package conformal Inference that implements all of the proposals we have introduced. In the spirit of reproducibility, all of our empirical results can also be easily (re)generated using this package.
Author	G'Sell, Max Wasserman, Larry Tibshirani, Ryan J. Lei, Jing Rinaldo, Alessandro
Author_xml	– sequence: 1 givenname: Jing orcidid: 0000-0003-3104-9387 surname: Lei fullname: Lei, Jing email: jinglei@andrew.cmu.edu organization: Department of Statistics, Carnegie Mellon University – sequence: 2 givenname: Max surname: G'Sell fullname: G'Sell, Max organization: Department of Statistics, Carnegie Mellon University – sequence: 3 givenname: Alessandro surname: Rinaldo fullname: Rinaldo, Alessandro organization: Department of Statistics, Carnegie Mellon University – sequence: 4 givenname: Ryan J. orcidid: 0000-0002-2158-8304 surname: Tibshirani fullname: Tibshirani, Ryan J. organization: Department of Statistics, Carnegie Mellon University – sequence: 5 givenname: Larry surname: Wasserman fullname: Wasserman, Larry organization: Department of Statistics, Carnegie Mellon University
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ContentType	Journal Article
Copyright	2018 American Statistical Association 2018 Copyright © 2018 American Statistical Association 2018 American Statistical Association
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Snippet	We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the... We develop a general framework for distribution-free predictive inference in regression, using conformai inference. The proposed methodology allows for the...
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SubjectTerms	Computational efficiency computer software Computing time Distribution-free Empirical analysis equations heteroskedasticity Inference Intervals Model misspecification prediction Prediction band Predictions Property Regression Regression analysis Reproducibility Statistical analysis Statistical methods Statistics Theory and Methods Variable importance Variants
Title	Distribution-Free Predictive Inference for Regression
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