  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.
