Why Calibration Error is Wrong Given Model Uncertainty: Using Posterior Predictive Checks with Deep Learning

TL;DR

This paper argues that calibration error is misleading when evaluating model uncertainty in deep learning, and advocates for posterior predictive checks to better assess what models truly know.

Contribution

It demonstrates that calibration error conflates model and aleatoric uncertainty, and shows how posterior predictive checks provide a more accurate evaluation method.

Findings

Calibration error often misleads in assessing model uncertainty.

Posterior predictive checks effectively evaluate model knowledge.

Misuse of calibration metrics can lead to incorrect trust in models.

Abstract

Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical metrics such as Prediction Interval Coverage Probability (PICP) and new metrics such as calibration error have entered the general repertoire of model evaluation in order to gain better insight into how the uncertainty of our model compares to reality. One important component of uncertainty modeling is model uncertainty (epistemic uncertainty), a measurement of what the model does and does not know. However, current evaluation techniques tends to conflate model uncertainty with aleatoric uncertainty (irreducible error), leading to incorrect conclusions. In this paper, using posterior predictive checks, we show how calibration error and its variants are almost always incorrect to use given model uncertainty, and further show how this mistake can lead to trust in bad models and mistrust in good models. Though posterior predictive checks has often been used for in-sample evaluation of Bayesian models, we show it still has an important place in the modern deep learning world.