# Powerful batch conformal prediction for classification

arXiv: https://arxiv.org/abs/2411.02239 · HTML: https://mlsanity.com/paper/2411.02239/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 4 Nov 2024.

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

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [With Malice Towards None: Assessing Uncertainty via Equalized Coverage](https://mlsanity.com/paper/1908.05428/) (2019)
- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [Choosing Between Methods of Combining p-values](https://mlsanity.com/paper/1707.06897/) (2017)
- [Adaptive novelty detection with false discovery rate guarantee](https://mlsanity.com/paper/2208.06685/) (2022)
- [Confidence on the Focal: Conformal Prediction with Selection-Conditional Coverage](https://mlsanity.com/paper/2403.03868/) (2024)
- [Selecting informative conformal prediction sets with false coverage rate control](https://mlsanity.com/paper/2403.12295/) (2024)
- [Batch Predictive Inference](https://mlsanity.com/paper/2409.13990/) (2024)
- [Simultaneous Control of All False Discovery Proportions in Large-Scale Multiple Hypothesis Testing](https://mlsanity.com/paper/1611.06739/) (2016)
- [Simultaneous directional inference](https://mlsanity.com/paper/2301.01653/) (2023)

## Built on by (most cited first, 4 of 4)

- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Class conditional conformal prediction for multiple inputs by p-value aggregation](https://mlsanity.com/paper/2507.07150/) (2025)
- [Synergistic Feature Fusion for Latent Lyrical Classification: A Gated Deep Learning Architecture](https://mlsanity.com/paper/2511.11673/) (2025)

## Abstract (arXiv)

In a split conformal framework with K classes, a calibration sample of n labeled examples is observed for inference on the label of a new unlabeled example. We explore the setting where a `batch' of m independent such unlabeled examples is given, and the goal is to construct a batch prediction set with 1-α coverage. Unlike individual prediction sets, the batch prediction set is a collection of label vectors of size m, while the calibration sample consists of univariate labels. A natural approach is to apply the Bonferroni correction, which concatenates individual prediction sets at level 1-α/m. We propose a uniformly more powerful solution, based on specific combinations of conformal p-values that exploit the Simes inequality. We provide a general recipe for valid inference with any combinations of conformal p-values, and compare the performance of several useful choices. Intuitively, the pooled evidence of relatively `easy' examples within the batch can help provide narrower batch prediction sets. Additionally, we introduce a more computationally intensive method that aggregates batch scores and can be even more powerful. The theoretical guarantees are established when all examples are independent and identically distributed (iid), as well as more generally when iid is assumed only conditionally within each class. Notably, our results remain valid under label distribution shift, since the distribution of the labels need not be the same in the calibration sample and in the new batch. The effectiveness of the methods is highlighted through illustrative synthetic and real data examples.