Universal Prediction Band via Semi-Definite Programming

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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

Tengyuan Liang. 2022. “Universal Prediction Band via Semi-Definite Programming.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 84 (4): 1558–1580.

@article{Liang_2022,
   title={Universal Prediction Band via Semi-Definite Programming},
   volume={84},
   ISSN={1467-9868},
   url={http://dx.doi.org/10.1111/rssb.12542},
   DOI={10.1111/rssb.12542},
   number={4},
   journal={Journal of the Royal Statistical Society Series B: Statistical Methodology},
   publisher={Oxford University Press (OUP)},
   author={Liang, Tengyuan},
   year={2022},
   month=aug, pages={1558–1580} }