Universal Prediction Band Via Semi-Definite Programming

We propose a computationally efficient method to construct nonparametric, heteroskedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. The data-adaptive band is universally applicable minimal distributional assumptions, strong non-asymptotic coverage properties, and easy implement using standard convex programs. Our approach can be viewed as novel variance interpolation confidence further leverages techniques from semi-definite programming sum-of-squares optimization. Theoretical numerical performances the proposed quantification are analyzed.