Distribution‐free prediction bands for non‐parametric regression
We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non‐parametric c...
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| Published in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 76; no. 1; pp. 71 - 96 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
Blackwell Publishers
2014
Blackwell Publishing Ltd John Wiley & Sons Ltd Oxford University Press |
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| ISSN: | 1369-7412, 1467-9868 |
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| Abstract | We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non‐parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data‐driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples. |
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| AbstractList | We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non‐parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data‐driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples. Summary We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of 'conformal prediction' with non-parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data-driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples. [PUBLICATION ABSTRACT] We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of 'conformal prediction' with non-parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data-driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples. Reprinted by permission of Blackwell Publishers Summary We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non‐parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data‐driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples. |
| Author | Lei, Jing Wasserman, Larry |
| Author_xml | – sequence: 1 fullname: Lei, Jing – sequence: 2 fullname: Wasserman, Larry |
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| References_xml | – reference: Shafer, G. and Vovk, V. (2008) A tutorial on conformal prediction. J. Mach. Learn. Res., 9, 371-421. – reference: Lei, J., Robins, J. and Wasserman, L. (2011) Distribution free prediction sets. J. Am. Statist. Ass, to be published. – reference: Rigollet, P. and Vert, R. (2009) Optimal rates for plug-in estimators of density level sets. Bernoulli, 14, 1154-1178. – reference: Ruppert, D., Wand, M. and Carroll, R. (2003) Semiparametric Regression. Cambridge: Cambridge University Press. – reference: Tukey, J. (1947) Nonparametric estimation: II, Statistical equivalent blocks and multivariate tolerance regions. Ann. Math. Statist., 18, 529-539. – reference: Rinaldo, A., Singh, A., Nugent, R. and Wasserman, L. (2012) Stability of density-based clustering. J. Mach. Learn. Res., 13, 905-948. – reference: Davidian, M. and Carroll, R. J. (1987) Variance function estimation. J. Am. Statist. 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| Snippet | We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions... We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions... Summary We study distribution‐free, non‐parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different... Summary We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different... |
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| SubjectTerms | Algorithms Approximation Conformal prediction Data analysis Distribution Estimation Finite sample property Forecasts Kernel density Oracles prediction Prediction bands Predictions probability distribution Samples Statistical analysis Statistics Studies |
| Title | Distribution‐free prediction bands for non‐parametric regression |
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