Universal Prediction Band via Semi-Definite Programming

TL;DR

This paper introduces a computationally efficient, nonparametric method for constructing heteroscedastic prediction bands that offer strong coverage guarantees and are applicable with minimal assumptions, providing an alternative to conformal prediction.

Contribution

The paper presents a novel variance interpolation method using semi-definite programming for uncertainty quantification, with theoretical guarantees and practical advantages over existing methods.

Findings

Strong non-asymptotic coverage properties

Easy implementation via convex programs

Applicable with minimal distributional assumptions

Abstract

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.