# Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage

arXiv: https://arxiv.org/abs/2502.17264 · HTML: https://mlsanity.com/paper/2502.17264/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 27 of 27)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [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)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [An Empirical Study of Rich Subgroup Fairness for Machine Learning](https://mlsanity.com/paper/1808.08166/) (2018)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Prediction Sets Adaptive to Unknown Covariate Shift](https://mlsanity.com/paper/2203.06126/) (2022)
- [Automatically Adaptive Conformal Risk Control](https://mlsanity.com/paper/2406.17819/) (2024)
- [Kandinsky Conformal Prediction: Efficient Calibration of Image Segmentation Algorithms](https://mlsanity.com/paper/2311.11837/) (2023)
- [Efficient Conformal Prediction under Data Heterogeneity](https://mlsanity.com/paper/2312.15799/) (2023)
- [Training-Conditional Coverage Bounds under Covariate Shift](https://mlsanity.com/paper/2405.16594/) (2024)

## Built on by (most cited first, 13 of 13)

- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [Efficient Federated Conformal Prediction with Group-Conditional Guarantee](https://mlsanity.com/paper/2603.14198/) (2026)
- [Conformal Prediction Adaptive to Unknown Subpopulation Shifts](https://mlsanity.com/paper/2506.05583/) (2025)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)
- [Beyond Aggregate Risk: Role-Stratified Conformal Risk Control for LLM Tool Calls](https://mlsanity.com/paper/2607.24343/) (2026)
- [Enhancing Conformal Prediction via Class Similarity](https://mlsanity.com/paper/2511.19359/) (2025)
- [Self-Organized Conformal Prediction: Reducing Regional Coverage Gaps with Unsupervised Group Discovery](https://mlsanity.com/paper/2606.29403/) (2026)
- [Certified Domain Consistency for Multi-Domain Retrieval: Label-Free Per-Domain Contamination Control with Conformal Risk Guarantees](https://mlsanity.com/paper/2607.14157/) (2026)
- [The Label Complexity of Useful Class-Conditional Prediction Sets under Distribution Shift](https://mlsanity.com/paper/2607.18088/) (2026)
- [Does Marginal Coverage Guarantee Class-Conditional Safety for Zero-Shot VLMs Under Shift?](https://mlsanity.com/paper/2608.19376/) (2026)
- [Multi-source conformal prediction: leveraging heterogeneity via localization](https://mlsanity.com/paper/2609.14531/) (2026)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

Conformal prediction is a powerful distribution-free framework for constructing prediction sets with coverage guarantees. Classical methods, such as split conformal prediction, provide marginal coverage, ensuring that the prediction set contains the label of a random test point with a target probability. However, these guarantees may not hold uniformly across different subpopulations, leading to disparities in coverage. Prior work has explored coverage guarantees conditioned on events related to the covariates and label of the test point. We present Kandinsky conformal prediction, a framework that significantly expands the scope of conditional coverage guarantees. In contrast to Mondrian conformal prediction, which restricts its coverage guarantees to disjoint groups -- reminiscent of the rigid, structured grids of Piet Mondrian's art -- our framework flexibly handles overlapping and fractional group memberships defined jointly on covariates and labels, reflecting the layered, intersecting forms in Wassily Kandinsky's compositions. Our algorithm unifies and extends existing methods, encompassing covariate-based group conditional, class conditional, and Mondrian conformal prediction as special cases, while achieving a minimax-optimal high-probability conditional coverage bound. Finally, we demonstrate the practicality of our approach through empirical evaluation on real-world datasets.