# E-Values Expand the Scope of Conformal Prediction

arXiv: https://arxiv.org/abs/2503.13050 · HTML: https://mlsanity.com/paper/2503.13050/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 24 of 24)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Human uncertainty makes classification more robust](https://mlsanity.com/paper/1908.07086/) (2019)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Tight Concentrations and Confidence Sequences from the Regret of Universal Portfolio](https://mlsanity.com/paper/2110.14099/) (2021)
- [Conformal prediction under ambiguous ground truth](https://mlsanity.com/paper/2307.09302/) (2023)
- [Conformal e-prediction](https://mlsanity.com/paper/2001.05989/) (2020)
- [Enhancing Conformal Prediction Using E-Test Statistics](https://mlsanity.com/paper/2403.19082/) (2024)
- [Post-selection inference for e-value based confidence intervals](https://mlsanity.com/paper/2203.12572/) (2022)
- [Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alpha](https://mlsanity.com/paper/2205.00901/) (2022)
- [On Confidence Sequences for Bounded Random Processes via Universal Gambling Strategies](https://mlsanity.com/paper/2207.12382/) (2022)
- [E-backtesting](https://mlsanity.com/paper/2209.00991/) (2022)

## Built on by (most cited first, 26 of 26)

- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Backward Conformal Prediction](https://mlsanity.com/paper/2505.13732/) (2025)
- [Conformal Selective Prediction with General Risk Control](https://mlsanity.com/paper/2603.24704/) (2026)
- [Adaptive Coverage Policies in Conformal Prediction](https://mlsanity.com/paper/2510.04318/) (2025)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Symmetric Aggregation of Conformity Scores for Efficient Uncertainty Sets](https://mlsanity.com/paper/2512.06945/) (2025)
- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [Fuzzy Prediction Sets: Conformal Prediction with E-values](https://mlsanity.com/paper/2509.13130/) (2025)
- [Fundamental bounds on efficiency-confidence trade-off for transductive conformal prediction](https://mlsanity.com/paper/2509.04631/) (2025)
- [E-Scores for (In)Correctness Assessment of Generative Model Outputs](https://mlsanity.com/paper/2510.25770/) (2025)
- [Certified Adaptive Refresh: Anytime-Valid Monitoring for Federated Conformal RAG](https://mlsanity.com/paper/2605.29139/) (2026)
- [When Can We Reuse a Calibration Set for Multiple Conformal Predictions?](https://mlsanity.com/paper/2506.19689/) (2025)
- [Conformal Prediction for Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2507.09678/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination](https://mlsanity.com/paper/2601.21324/) (2026)
- [Improving Backward Conformal Prediction via Non-Conformity Score Transformation](https://mlsanity.com/paper/2602.01733/) (2026)
- [Time-uniform conformal and PAC prediction](https://mlsanity.com/paper/2602.06297/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables](https://mlsanity.com/paper/2604.11305/) (2026)
- [Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models](https://mlsanity.com/paper/2605.18202/) (2026)
- [Set-Preserving Calibration from Conformal P-Values to E-Values](https://mlsanity.com/paper/2606.03600/) (2026)
- [Bentkus-type asymptotic e-values](https://mlsanity.com/paper/2606.06332/) (2026)
- [Rolling Conformal Prediction in Sequential Model Training](https://mlsanity.com/paper/2609.26951/) (2026)
- [Counterfactual Online Conformal Prediction Under Adaptive Logging](https://mlsanity.com/paper/2609.30811/) (2026)
- [SLICE: Sequential Likelihood-Free Inference via Conformal E-Values](https://mlsanity.com/paper/2610.13855/) (2026)
- [Backward Conformal Prediction under Covariate Shift](https://mlsanity.com/paper/2610.16048/) (2026)

## Abstract (arXiv)

Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future test point cannot be too extreme relative to a calibration set. This rank-based method can be reformulated in terms of p-values. In this paper, we explore an alternative approach based on e-values, known as conformal e-prediction. E-values offer key advantages that cannot be achieved with p-values, enabling new theoretical and practical capabilities. In particular, we present three applications that leverage the unique strengths of e-values: batch anytime-valid conformal prediction, fixed-size conformal sets with data-dependent coverage, and conformal prediction under ambiguous ground truth. Overall, these examples demonstrate that e-value-based constructions provide a flexible expansion of the toolbox of conformal prediction.