Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity concepts

TL;DR

This paper reviews and introduces validation methods for uncertainty quantification in machine learning, emphasizing the concepts of consistency and adaptivity to better assess UQ metrics across input ranges.

Contribution

It provides a unified framework based on consistency and adaptivity for evaluating UQ validation methods, enhancing understanding of their capabilities.

Findings

Validation methods are derived from basic rules.

Methods are tested on synthetic and real datasets.

The framework improves assessment of UQ metrics' reliability.

Abstract

The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves) which explore complementary aspects of calibration, without covering all the desirable ones. For instance, none of these methods deals with the reliability of UQ metrics across the range of input features (adaptivity). Based on the complementary concepts of consistency and adaptivity, the toolbox of common validation methods for variance- and intervals- based UQ metrics is revisited with the aim to provide a better grasp on their capabilities. This study is conceived as an introduction to UQ validation, and all methods are derived from a few basic rules. The methods are illustrated and tested on synthetic datasets and representative examples extracted from the recent physico-chemical machine learning UQ literature.