# Probabilistic Conformal Prediction with Approximate Conditional Validity

arXiv: https://arxiv.org/abs/2407.01794 · HTML: https://mlsanity.com/paper/2407.01794/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 23 of 23)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Accelerated Hierarchical Density Clustering](https://mlsanity.com/paper/1705.07321/) (2017)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [With Malice Towards None: Assessing Uncertainty via Equalized Coverage](https://mlsanity.com/paper/1908.05428/) (2019)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [Group-Conditional Conformal Prediction via Quantile Regression Calibration for Crop and Weed Classification](https://mlsanity.com/paper/2308.15094/) (2023)
- [Conformalized Unconditional Quantile Regression](https://mlsanity.com/paper/2304.01426/) (2023)
- [Adaptive Conformal Regression with Jackknife+ Rescaled Scores](https://mlsanity.com/paper/2305.19901/) (2023)
- [Conformalized Deep Splines for Optimal and Efficient Prediction Sets](https://mlsanity.com/paper/2311.00774/) (2023)

## Built on by (most cited first, 23 of 23)

- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Conditional Coverage Diagnostics for Conformal Prediction](https://mlsanity.com/paper/2512.11779/) (2025)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Conformal Prediction Meets Long-tail Classification](https://mlsanity.com/paper/2508.11345/) (2025)
- [JAPAN: Joint Adaptive Prediction Areas with Normalising-Flows](https://mlsanity.com/paper/2505.23196/) (2025)
- [Colorful Pinball: Density-Weighted Quantile Regression for Conditional Guarantee of Conformal Prediction](https://mlsanity.com/paper/2512.24139/) (2025)
- [CLAPS: Aleatoric-Epistemic Scaling via Last-Layer Laplace for Conformal Regression](https://mlsanity.com/paper/2512.01384/) (2025)
- [Adaptive Cumulative Mass Calibration with Conformal Prediction](https://mlsanity.com/paper/2505.15437/) (2025)
- [Provably Minimum-Length Conformal Prediction Sets for Ordinal Classification](https://mlsanity.com/paper/2511.16845/) (2025)
- [Beyond Surface Statistics: Robust Conformal Prediction for LLMs via Internal Representations](https://mlsanity.com/paper/2604.16217/) (2026)
- [A Kernel Nonconformity Score for Multivariate Conformal Prediction](https://mlsanity.com/paper/2604.21595/) (2026)
- [Conformalized Percentile Interval: Finite Sample Validity and Improved Conditional Performance](https://mlsanity.com/paper/2605.03233/) (2026)
- [CoVeR: Conformal Calibration for Versatile and Reliable Autoregressive Next-Token Prediction](https://mlsanity.com/paper/2509.04733/) (2025)
- [Leverage-Weighted Conformal Prediction](https://mlsanity.com/paper/2602.12693/) (2026)
- [Super-Level-Set Regression: Conditional Quantiles via Volume Minimization](https://mlsanity.com/paper/2605.06210/) (2026)
- [Conformal Reliability: A New Evaluation Metric for Conditional Generation](https://mlsanity.com/paper/2605.30807/) (2026)
- [Robust Bayes-Assisted Conformal Prediction](https://mlsanity.com/paper/2607.04236/) (2026)
- [View-Structured Conformal Prediction for 3D Gaussian Splatting](https://mlsanity.com/paper/2609.10307/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)
- [How Synthetic Labels Improve Conformal Prediction: A Perspective on Conditional Coverage](https://mlsanity.com/paper/2609.33482/) (2026)

## Abstract (arXiv)

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution PY mid X. Existing methods, such as conformalized quantile regression and probabilistic conformal prediction, usually provide only a marginal coverage guarantee. In contrast, our approach extends these frameworks to achieve approximately conditional coverage, which is crucial for many practical applications. Our prediction sets adapt to the behavior of the predictive distribution, making them effective even under high heteroscedasticity. While exact conditional guarantees are infeasible without assumptions on the underlying data distribution, we derive non-asymptotic bounds that depend on the total variation distance of the conditional distribution and its estimate. Using extensive simulations, we show that our method consistently outperforms existing approaches in terms of conditional coverage, leading to more reliable statistical inference in a variety of applications.