# UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

arXiv: https://arxiv.org/abs/2306.16549 · HTML: https://mlsanity.com/paper/2306.16549/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 63 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Deep Network Approximation for Smooth Functions](https://mlsanity.com/paper/2001.03040/) (2020)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [How do noise tails impact on deep ReLU networks?](https://mlsanity.com/paper/2203.10418/) (2022)
- [Flexible Model Aggregation for Quantile Regression](https://mlsanity.com/paper/2103.00083/) (2021)
- [Learning Prediction Intervals for Regression: Generalization and Calibration](https://mlsanity.com/paper/2102.13625/) (2021)
- [Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension](https://mlsanity.com/paper/2302.05851/) (2023)
- [Universal Prediction Band via Semi-Definite Programming](https://mlsanity.com/paper/2103.17203/) (2021)

## Built on by (most cited first, 8 of 8)

- [Conformal online model aggregation](https://mlsanity.com/paper/2403.15527/) (2024)
- [Robust Uncertainty Quantification Using Conformalised Monte Carlo Prediction](https://mlsanity.com/paper/2308.09647/) (2023)
- [Parametric Scaling Law of Tuning Bias in Conformal Prediction](https://mlsanity.com/paper/2502.03023/) (2025)
- [Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift](https://mlsanity.com/paper/2405.10302/) (2024)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)
- [Data-light Uncertainty Set Merging with Admissibility](https://mlsanity.com/paper/2410.12201/) (2024)
- [Beyond Accuracy: Reliability and Uncertainty Estimation in Convolutional Neural Networks](https://mlsanity.com/paper/2603.10731/) (2026)
- [Distribution-Aware Conformal Prediction: A Framework for generating efficient prediction intervals for time series](https://mlsanity.com/paper/2605.26569/) (2026)

## Abstract (arXiv)

Uncertainty quantification in prediction presents a compelling challenge with vast applications across various domains, including biomedical science, economics, and weather forecasting. There exists a wide array of methods for constructing prediction intervals, such as quantile regression and conformal prediction. However, practitioners often face the challenge of selecting the most suitable method for a specific real-world data problem. In response to this dilemma, we introduce a novel and universally applicable strategy called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). This technique excels in efficiently aggregating multiple prediction intervals while maintaining a small average width of the prediction band and ensuring coverage. UTOPIA is grounded in linear or convex programming, making it straightforward to train and implement. In the specific case where the prediction methods are elementary basis functions, as in kernel and spline bases, our method becomes the construction of a prediction band. Our proposed methodologies are supported by theoretical guarantees on the coverage probability and the average width of the aggregated prediction interval, which are detailed in this paper. The practicality and effectiveness of UTOPIA are further validated through its application to synthetic data and two real-world datasets in finance and macroeconomics.