Universal prediction band via semi-definite programming
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2022 · Volume 84 · Issue 4
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 analysed.
Keywords
heteroscedasticity, nonparametric prediction band, semi-definite programming, sum-of-squares, uncertainty quantification
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