# A Kernel Nonconformity Score for Multivariate Conformal Prediction

Source: [A Kernel Nonconformity Score for Multivariate Conformal Prediction](<https://www.sota2.com/research/paper/69eaf93755a3c32af89f8adc>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-04-25T05:00:04.396Z

Authors: Louis Meyer, Wenkai Xu

Published: 2026-04-23T12:19:21.000Z

## Abstract

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS) that produces prediction regions that explicitly adapt to this geometry. We show that the proposed score resembles the Gaussian process posterior variance, unifying Bayesian uncertainty quantification with the coverage guarantees of frequentist-type. Moreover, the MKS can be decomposed into an anisotropic Maximum Mean Discrepancy (MMD) that interpolates between kernel density estimation and covariance-weighted distance. We prove finite-sample coverage guarantees and establish convergence rates that depend on the effective rank of the kernel-based covariance operator rather than the ambient dimension, enabling dimension-free adaptation. On regression tasks, the MKS reduces the volume of prediction region significantly, compared to ellipsoidal baselines while maintaining nominal coverage, with larger gains at higher dimensions and tighter coverage levels.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Multivariate Regression on House (real data)](<https://www.sota2.com/research/sota/multivariate-regression-on-house-real-data.md>): Multivariate Regression; House (real data); Volume Ratio (1-alpha=0.90): 95.057.

- [Multivariate Regression on Bio (real data)](<https://www.sota2.com/research/sota/multivariate-regression-on-bio-real-data.md>): Multivariate Regression; Bio (real data); Volume Ratio (1-alpha=.90): 0.53949.

- [Multivariate Regression on Blog (real data)](<https://www.sota2.com/research/sota/multivariate-regression-on-blog-real-data.md>): Multivariate Regression; Blog (real data); Volume Ratio (1-alpha=0.90): 59.225.

- [Prediction Region Estimation on Synthetic data 100 seeds (test)](<https://www.sota2.com/research/sota/prediction-region-estimation-on-synthetic-data-100-seeds-test.md>): Prediction Region Estimation; Synthetic data 100 seeds (test); Coverage: 99.002.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2604.21595>)

[PDF](<https://arxiv.org/pdf/2604.21595.pdf>)