Universal Prediction Band via Semi-Definite Programming

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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.

Citation

Tengyuan Liang. 2022. “Universal Prediction Band via Semi-Definite Programming.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84 (4): 1558–1580.

@article{Liang2022,
  title = {Universal Prediction Band via Semi-Definite Programming},
  author = {Liang, Tengyuan},
  journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume = {84},
  number = {4},
  pages = {1558--1580},
  year = {2022},
  month = aug,
  publisher = {Oxford University Press (OUP)},
  issn = {1467-9868},
  doi = {10.1111/rssb.12542},
  url = {http://dx.doi.org/10.1111/rssb.12542},
}