Hierarchical Utility Calibration for Structured Multiclass Decisions

A key factor in deciding whether to trust an automatic prediction is its confidence score, which should be calibrated to match the actual probability of the prediction being correct. Most confidence calibration metrics target binary or multi-class tasks, while multi-label calibration remains largely underexplored. Multi-label classification tasks, such as assigning medical codes to clinical notes or determining news topics, are usually dominated by a large number of negatives, i.e., labels that do not apply. We show that existing binning schemes to compute label-wise expected calibration error either underestimate the error, simply reflect label frequency, or suffer from many bins with very few instances. To achieve trustworthy label-wise calibration errors, we propose a new binning scheme that gives equal weight to positive and negative label assignments. Our empirical study demonstrates that in contrast to existing binning schemes, our new scheme results in meaningful estimates of calibration error in hierarchical and in extreme multi-label classification. We also show that calibrating confidence scores of large language models for multi-label predictions is an open challenge. Our detailed analysis lays the foundation for further research by providing a solid evaluation metric for measuring calibration in multi-label classification.

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.