Evaluating the Quality of the Quantified Uncertainty for (Re)Calibration of Data-Driven Regression Models

TL;DR

This paper systematically evaluates various regression calibration metrics, revealing inconsistencies and identifying the most reliable ones, to improve the assessment of uncertainty estimates in safety-critical models.

Contribution

It categorizes and benchmarks regression calibration metrics independently of models, highlighting their inconsistencies and proposing the most dependable metrics.

Findings

Calibration metrics often produce conflicting results.

Many metrics disagree on the same recalibration outcome.

ENCE and CWC are identified as the most reliable metrics.

Abstract

In safety-critical applications data-driven models must not only be accurate but also provide reliable uncertainty estimates. This property, commonly referred to as calibration, is essential for risk-aware decision-making. In regression a wide variety of calibration metrics and recalibration methods have emerged. However, these metrics differ significantly in their definitions, assumptions and scales, making it difficult to interpret and compare results across studies. Moreover, most recalibration methods have been evaluated using only a small subset of metrics, leaving it unclear whether improvements generalize across different notions of calibration. In this work, we systematically extract and categorize regression calibration metrics from the literature and benchmark these metrics independently of specific modelling methods or recalibration approaches. Through controlled experiments with real-world, synthetic and artificially miscalibrated data, we demonstrate that calibration metrics frequently produce conflicting results. Our analysis reveals substantial inconsistencies: many metrics disagree in their evaluation of the same recalibration result, and some even indicate contradictory conclusions. This inconsistency is particularly concerning as it potentially allows cherry-picking of metrics to create misleading impressions of success. We identify the Expected Normalized Calibration Error (ENCE) and the Coverage Width-based Criterion (CWC) as the most dependable metrics in our tests. Our findings highlight the critical role of metric selection in calibration research.