# Universal Prediction Band via Semi-Definite Programming

arXiv: https://arxiv.org/abs/2103.17203 · HTML: https://mlsanity.com/paper/2103.17203/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-ℓ1-Norm Interpolated Classifiers](https://mlsanity.com/paper/2002.01586/) (2020)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [Interpolating Classifiers Make Few Mistakes](https://mlsanity.com/paper/2101.11815/) (2021)
- [Shape-Constrained Regression using Sum of Squares Polynomials](https://mlsanity.com/paper/2004.03853/) (2020)

## Built on by (most cited first, 2 of 2)

- [UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation](https://mlsanity.com/paper/2306.16549/) (2023)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)

## Abstract (arXiv)

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.