Universal Prediction Band via Semi-Definite Programming

Tengyuan Liang

Papers from arXiv.org

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.

Date: 2021-03, Revised 2023-01
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Published in Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84(4):1558-1580, 2022

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