Nonparametric Distribution Regression Re-calibration

TL;DR

This paper introduces a nonparametric re-calibration method for probabilistic regression that improves calibration accuracy without restrictive assumptions, using kernel mean embeddings for efficient and reliable uncertainty estimation.

Contribution

It proposes a novel nonparametric re-calibration algorithm based on conditional kernel mean embeddings, with a new characteristic kernel enabling efficient inference for real-valued targets.

Findings

Outperforms prior re-calibration methods across diverse benchmarks

Achieves calibration correction without restrictive parametric assumptions

Provides efficient inference with $ ext{O}(n ext{log} n)$ complexity

Abstract

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration, producing narrow but overconfident predictions. However, in safety-critical settings, trustworthy uncertainty estimates are often more valuable than narrow intervals. Realizing the problem, several recent works have focused on post-hoc corrections; however, existing methods either rely on weak notions of calibration (such as PIT uniformity) or impose restrictive parametric assumptions on the nature of the error. To address these limitations, we propose a novel nonparametric re-calibration algorithm based on conditional kernel mean embeddings, capable of correcting calibration error without restrictive modeling assumptions. For efficient inference with real-valued targets, we introduce a novel characteristic kernel over distributions that can be evaluated in $\mathcal{O}(n \log n)$ time for empirical distributions of size $n$. We demonstrate that our method consistently outperforms prior re-calibration approaches across a diverse set of regression benchmarks and model classes.