Divide et Calibra: Multiclass Local Calibration via Vector Quantization
Authors: Cesare Barbera, Lorenzo Perini, Giovanni De Toni, Andrea Passerini, Andrea Pugnana
Organizations: University of Pisa, Univeristy of Trento · Meta · Fondazione Bruno Kessler · University of Trento
Abstract
Accurate and well-calibrated Machine Learning (ML) models are mandatory in high-stakes settings, yet effective multiclass calibration remains challenging: global approaches assume calibration errors are homogeneous across the latent space, while local methods often rely on latent-space dimensionality reduction, which leads to information loss. To address these issues, we propose a compositional approach to multiclass calibration, where region-specific calibration maps are constructed from shared codeword-dependent factors. We instantiate this idea via Vector Quantization (VQ), which induces a structured partition of the representation space, and an indexed parameterization of Dirichlet concentrations that enables parameter sharing across regions. Our approach learns heterogeneous calibration maps that generalize well even to sparse regions of the latent space. Experiments on benchmark datasets show significant improvements in local calibration while maintaining competitive global calibration and predictive performance.
Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We introduce a large-scale, standardized benchmark for post-hoc calibration, covering nearly 2000 experiments across tabular and computer vision tasks, including binary, multiclass, and large-scale classification settings. Our benchmark aggregates predictions from a diverse set of classical models, modern deep learning architectures, and foundation models, and provides unified, reproducible implementations of dozens of calibration methods within a common evaluation framework. We argue that Post-Hoc Improvement (PHI) in proper scoring rules offers a principled alternative to traditional calibration error estimators for comparing post-hoc methods, capturing both calibration quality and potential degradation to the model's predictive performance. Using this framework, we conduct the most comprehensive empirical study of post-hoc calibration to date. Our results reveal consistent patterns across domains: smooth calibration functions outperform binning-based approaches, dedicated multiclass methods are essential in high-dimensional settings, and generic machine learning models are not competitive without calibration-specific design. To facilitate future research, we release all data, code, and evaluation tools, providing a plug-and-play benchmark for developing and comparing calibration methods.
Reliable probability estimates by classifiers are essential in high-risk applications. In practice, however, predicted probabilities are often miscalibrated, and many existing post-hoc calibration methods typically lack guarantees that a specific notion of calibration is achieved after the correction procedure is applied. We introduce a set-based perspective on calibration through the notion of cumulative mass calibration and the corresponding error measures. We propose a new calibration procedure based on conformal prediction that forms cumulative probabilities with guaranteed marginal coverage. We introduce an adaptive temperature scaling algorithm, with the temperature tuned for each input to satisfy the conformal coverage constraint. As we show, this procedure can be efficiently implemented. Across image classification tasks, particularly in settings with many classes, our method improves newly introduced calibration error measures (CMCE and α-CMCE) and standard metrics (such as ECE, cw-ECE, MCE) over the existing baselines.
Reliable evaluation of vision-language models (VLMs) and medical vision-language models (Medical-VLMs) requires calibrated confidence, particularly under realistic clinical conditions. However, existing efforts mainly focused on improving accuracy, leaving calibration in the medical domain underexplored. To this end, we propose MVC-Bench, a calibration-centric benchmark for medical image classification with VLMs and Medical-VLMs. MVC-Bench assesses the calibration across three axes: (i) robustness to modality, backbone, and domain shift (ii) effectiveness of calibration strategies and prompt-tuning methods (iii) stability under prompt-template and random-seed variations. The benchmark covers eight different backbones, three medical modalities, including fundus imaging, histopathology, and chest X-ray under in-domain and domain shift settings. It compares post-hoc calibration, train-time calibration, and zero-shot inference methods, together with six prompt-tuning methods. Across more than 1638 controlled experiments, we report accuracy and Expected Calibration Error (ECE) as primary metrics, and further report results with complementary calibration measures, including Maximum Calibration Error (MCE) and Adaptive Calibration Error (ACE). We further investigate the underlying causes of miscalibration in VLMs and Medical-VLMs and propose a simple train-time calibration method, Multi-Class Margin (MCM) regularization, which achieves lowest ECE on 10 out of 12 settings in in-domain and remains competitive under domain shifts. Collectively, MVC-Bench provides a structured evaluation framework and actionable guidance for improving calibration in safety-critical medical workflows.