PAC-Bayes Analysis for Recalibration in Classification

TL;DR

This paper introduces a PAC-Bayes-based theoretical framework for calibration error analysis in multiclass classification, providing the first optimizable generalization bound and a new recalibration algorithm that improves Gaussian process calibration.

Contribution

It extends calibration analysis from binary to multiclass classification and proposes a theoretically grounded recalibration method with empirical validation.

Findings

Theoretical generalization bound for calibration error in multiclass classification.

Proposed recalibration algorithm improves Gaussian process calibration performance.

Empirical results demonstrate enhanced calibration across multiple datasets.

Abstract

Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary classification, creating a significant gap with practical applications such as multiclass classification. Additionally, many parametric recalibration algorithms lack theoretical guarantees for their generalization performance. To address these issues, we conduct a generalization analysis of calibration error using the probably approximately correct Bayes framework. This approach enables us to derive the first optimizable upper bound for generalization error in the calibration context. On the basis of our theory, we propose a generalization-aware recalibration algorithm. Numerical experiments show that our algorithm enhances the performance of Gaussian process-based recalibration across various benchmark datasets and models.