# Data-light Uncertainty Set Merging with Admissibility

arXiv: https://arxiv.org/abs/2410.12201 · HTML: https://mlsanity.com/paper/2410.12201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [One-Shot Federated Conformal Prediction](https://mlsanity.com/paper/2302.06322/) (2023)
- [Efficient and Differentiable Conformal Prediction with General Function Classes](https://mlsanity.com/paper/2202.11091/) (2022)
- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (2021)
- [Multi Split Conformal Prediction](https://mlsanity.com/paper/2103.00627/) (2021)
- [Choosing Between Methods of Combining p-values](https://mlsanity.com/paper/1707.06897/) (2017)
- [Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms](https://mlsanity.com/paper/2001.08877/) (2020)
- [Learning Prediction Intervals for Regression: Generalization and Calibration](https://mlsanity.com/paper/2102.13625/) (2021)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Randomized and Exchangeable Improvements of Markov's, Chebyshev's and Chernoff's Inequalities](https://mlsanity.com/paper/2304.02611/) (2023)
- [Conformal prediction after data-dependent model selection](https://mlsanity.com/paper/2408.07066/) (2024)
- [Derandomized knockoffs: leveraging e-values for false discovery rate control](https://mlsanity.com/paper/2205.15461/) (2022)
- [UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation](https://mlsanity.com/paper/2306.16549/) (2023)

## Abstract (arXiv)

This article introduces a Synthetics, Aggregation, and Test inversion (SAT) approach for merging diverse and potentially dependent uncertainty sets into a single unified set. The procedure is data-light, relying only on initial sets and their nominal levels, and it flexibly adapts to user-specified input sets with possibly varying coverage guarantees. SAT is motivated by the challenge of integrating uncertainty sets when only the initial sets and their control levels are available-for example, when merging confidence sets from distributed sites under communication constraints or combining conformal prediction sets generated by different algorithms or data splits. To address this, SAT constructs and aggregates novel synthetic test statistics, and then derive merged sets through test inversion. Our method leverages the duality between set estimation and hypothesis testing, ensuring reliable coverage in dependent scenarios. A key theoretical contribution is a rigorous analysis of SAT's properties, including its admissibility in the context of deterministic set merging. Both theoretical analyses and empirical results confirm the method's finite-sample coverage validity and desirable set sizes.