Universal prediction band via semi‐definite programming

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.