# Transductive conformal inference with adaptive scores

arXiv: https://arxiv.org/abs/2310.18108 · HTML: https://mlsanity.com/paper/2310.18108/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 14 of 14)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Universal distribution of the empirical coverage in split conformal prediction](https://mlsanity.com/paper/2303.02770/) (2023)
- [Selective conformal inference with false coverage-statement rate control](https://mlsanity.com/paper/2301.00584/) (2023)
- [Post-selection Inference for Conformal Prediction: Trading off Coverage for Precision](https://mlsanity.com/paper/2304.06158/) (2023)
- [Simultaneous false discovery proportion bounds via knockoffs and closed testing](https://mlsanity.com/paper/2212.12822/) (2022)

## Built on by (most cited first, 21 of 21)

- [Conformal Prediction for Zero-Shot Models](https://mlsanity.com/paper/2505.24693/) (2025)
- [Backward Conformal Prediction](https://mlsanity.com/paper/2505.13732/) (2025)
- [Selecting informative conformal prediction sets with false coverage rate control](https://mlsanity.com/paper/2403.12295/) (2024)
- [General Synthetic-Powered Inference](https://mlsanity.com/paper/2509.20345/) (2025)
- [Powerful batch conformal prediction for classification](https://mlsanity.com/paper/2411.02239/) (2024)
- [Transductive Conformal Inference for Full Ranking](https://mlsanity.com/paper/2501.11384/) (2025)
- [Fundamental bounds on efficiency-confidence trade-off for transductive conformal prediction](https://mlsanity.com/paper/2509.04631/) (2025)
- [Conformal Prediction via Transported Beta Laws](https://mlsanity.com/paper/2605.19024/) (2026)
- [Data-Adaptive Tradeoffs among Multiple Risks in Distribution-Free Prediction](https://mlsanity.com/paper/2403.19605/) (2024)
- [Conformal Data Contamination Tests for In-distribution Data Acquisition](https://mlsanity.com/paper/2507.13835/) (2025)
- [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)
- [Conformal Path Reasoning: Trustworthy Knowledge Graph Question Answering via Path-Level Calibration](https://mlsanity.com/paper/2605.08077/) (2026)
- [RoCP-GNN: Robust Conformal Prediction for Graph Neural Networks in Node-Classification](https://mlsanity.com/paper/2408.13825/) (2024)
- [Class conditional conformal prediction for multiple inputs by p-value aggregation](https://mlsanity.com/paper/2507.07150/) (2025)
- [Distribution-informed Efficient Conformal Prediction for Full Ranking](https://mlsanity.com/paper/2601.23128/) (2026)
- [Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference](https://mlsanity.com/paper/2605.20726/) (2026)
- [Conformal calibration and look-elsewhere effect in anomaly detection for new-physics searches](https://mlsanity.com/paper/2606.13780/) (2026)
- [Learning Topology-Aware Representations via Test-Time Adaptation for Anomaly Segmentation](https://mlsanity.com/paper/2606.28268/) (2026)
- [Occupancy-based Quantile Risk Control](https://mlsanity.com/paper/2609.03104/) (2026)
- [Calibration Count Reuse: Validity Does Not Determine Efficiency](https://mlsanity.com/paper/2609.25138/) (2026)

## Abstract (arXiv)

Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of m new points, giving rise to m conformal p-values. While classical results only concern their marginal distribution, we show that their joint distribution follows a P'olya urn model, and establish a concentration inequality for their empirical distribution function. The results hold for arbitrary exchangeable scores, including adaptive ones that can use the covariates of the test+calibration samples at training stage for increased accuracy. We demonstrate the usefulness of these theoretical results through uniform, in-probability guarantees for two machine learning tasks of current interest: interval prediction for transductive transfer learning and novelty detection based on two-class classification.