  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 prediction band
is universally applicable with minimal distributional assumptions, with strong
non-asymptotic coverage properties, and 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.
