Universal Prediction Band via Semi-Definite Programming

• URL: http://arxiv.org/abs/2103.17203v1
• Date: Wed, 31 Mar 2021 16:30:58 GMT
• Title: Universal Prediction Band via Semi-Definite Programming
• Authors: Tengyuan Liang
• Abstract summary: We propose a method to construct nonparametric, heteroskedastic prediction bands for uncertainty quantification. The data-adaptive prediction band is universally applicable with minimal distributional assumptions.
• Score: 4.401255328572734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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