Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation

TL;DR

This paper critically examines the limitations of current loss-based methods for quantifying epistemic uncertainty in machine learning, revealing that they fail to accurately represent the learner's lack of knowledge.

Contribution

It provides a theoretical analysis showing that loss minimisation does not incentivise second-order learners to faithfully represent epistemic uncertainty.

Findings

Loss functions for second-order predictors are ineffective

Standard loss minimisation does not capture epistemic uncertainty accurately

Second-order learners may not reflect true model uncertainty

Abstract

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.