On Information-Theoretic Measures of Predictive Uncertainty
This work addresses the lack of consensus on uncertainty quantification for high-stakes ML applications, providing insights into measure selection, but it is incremental as it builds on existing concepts without introducing a fundamentally new paradigm.
The authors tackled the problem of quantifying predictive uncertainty in machine learning by proposing a framework that categorizes measures based on the predicting model and approximation of the true distribution, evaluating them across tasks to show that alignment with the model is crucial for in-distribution data and that epistemic uncertainty measures have limitations for out-of-distribution data.
Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.