# A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression

arXiv: https://arxiv.org/abs/2501.10533 · HTML: https://mlsanity.com/paper/2501.10533/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2025.

## Built on by (most cited first, 24 of 24)

- [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)
- [CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference](https://mlsanity.com/paper/2508.17077/) (2025)
- [Multivariate Latent Recalibration for Conditional Normalizing Flows](https://mlsanity.com/paper/2505.16636/) (2025)
- [Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks](https://mlsanity.com/paper/2508.11025/) (2025)
- [Neural Optimal Transport Meets Multivariate Conformal Prediction](https://mlsanity.com/paper/2509.25444/) (2025)
- [A Gentle Introduction to Conformal Time Series Forecasting](https://mlsanity.com/paper/2511.13608/) (2025)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization](https://mlsanity.com/paper/2512.15383/) (2025)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [Conformal Graph Prediction with Z-Gromov-Wasserstein Distances](https://mlsanity.com/paper/2603.02460/) (2026)
- [Multivariate Uncertainty Quantification with Tomographic Quantile Forests](https://mlsanity.com/paper/2512.16383/) (2025)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [A Kernel Nonconformity Score for Multivariate Conformal Prediction](https://mlsanity.com/paper/2604.21595/) (2026)
- [Risk-Based Thresholding for Reliable Anomaly Detection in Concentrated Solar Power Plants](https://mlsanity.com/paper/2503.19146/) (2025)
- [Km-scale dynamical downscaling through conformalized latent diffusion models](https://mlsanity.com/paper/2510.13301/) (2025)
- [Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularization](https://mlsanity.com/paper/2510.21273/) (2025)
- [What You See is (Usually) What You Get: Multimodal Prototype Networks that Abstain from Expensive Modalities](https://mlsanity.com/paper/2511.19752/) (2025)
- [Calibrated uncertainty quantification for prosumer flexibility aggregation in ancillary service markets](https://mlsanity.com/paper/2601.14663/) (2026)
- [When Is a Conformal Guarantee Fair? Auditing Silent Subgroup Under-Coverage in Alzheimer's Disease Longitudinal Prediction](https://mlsanity.com/paper/2608.04254/) (2026)
- [Exact Risk-Complexity Laws for Projective Boundaries in Scenario Optimization and Distribution-Free Certification](https://mlsanity.com/paper/2609.01355/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)
- [Conformal Prediction and Conditional Coverage for Tabular Foundation Models](https://mlsanity.com/paper/2609.34887/) (2026)

## Abstract (arXiv)

Conformal prediction provides a powerful framework for constructing distribution-free prediction regions with finite-sample coverage guarantees. While extensively studied in univariate settings, its extension to multi-output problems presents additional challenges, including complex output dependencies and high computational costs, and remains relatively underexplored. In this work, we present a unified comparative study of nine conformal methods with different multivariate base models for constructing multivariate prediction regions within the same framework. This study highlights their key properties while also exploring the connections between them. Additionally, we introduce two novel classes of conformity scores for multi-output regression that generalize their univariate counterparts. These scores ensure asymptotic conditional coverage while maintaining exact finite-sample marginal coverage. One class is compatible with any generative model, offering broad applicability, while the other is computationally efficient, leveraging the properties of invertible generative models. Finally, we conduct a comprehensive empirical evaluation across 13 tabular datasets, comparing all the multi-output conformal methods explored in this work. To ensure a fair and consistent comparison, all methods are implemented within a unified code base.