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Universal Prediction Band via Semi-Definite Programming

Tengyuan Liang

arXiv 31 Mar 2021 · Statistics — Machine Learning · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2022) · 1 citations (OpenAlex)

arXiv:2103.17203 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, has strong non-asymptotic coverage properties, and is easy to implement using standard convex programs. Our approach can be viewed as a novel variance interpolation with confidence and further leverages techniques from semi-definite programming and sum-of-squares optimization. Theoretical and numerical performances for the proposed approach for uncertainty quantification are analyzed.

Citation extraction

29
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42
in-text mentions
29
distinct cited
4
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9,673
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Jing Lei, Max G'Sell, Alessandro Rinaldo, Ryan J. Tibshirani, and La… (2017) Distribution-Free Predictive Inference for Regression0.81142100%
2Yaniv Romano, Evan Patterson, and Emmanuel Candes (2019) Conformalized Quantile Regression0.81142100%
3Tengyuan Liang and Alexander Rakhlin (2020) Ridgeless self0.7373367%
4Glenn Shafer and Vladimir Vovk (2008) A Tutorial on Conformal Prediction0.58531100%
5J Andrew Bagnell and Amir-massoud Farahmand (2015) Learning positive functions in a hilbert space0.51121100%
6Ulysse Marteau-Ferey, Francis Bach, and Alessandro Rudi (2020) Non-parametric Models for Non-negative Functions0.51121100%
7Vladimir Vovk, Alex Gammerman, and Glenn Shafer (2005) Algorithmic learning in a random world0.51121100%
8Peter Bartlett, Yoav Freund, Wee Sun Lee, and Robert E. Schapire Boosting the margin: A new explanation for the effectiveness of voting methods0.40511100%
9Peter L. Bartlett, Philip M. Long, Gábor Lugosi, and Alexander Tsigler (2020) Benign overfitting in linear regression0.40511100%
10Peter L. Bartlett, Andrea Montanari, and Alexander Rakhlin (2021) Deep learning: A statistical viewpoint0.40511100%

Showing the top 10 of 29 scored citations.