UNIVERSAL PREDICTION BAND, VARIANCE INTERPOLATION, AND SEMI-DEFINITE PROGRAMMING
TENGYUAN LIANG – UNIVERSITY OF CHICAGO
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.
Liang, Tengyuan. “Universal Prediction Band via Semi‐definite Programming.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 84, no. 4 (September 2022): 1558–80. https://doi.org/10.1111/rssb.12542.