Evidential Uncertainty Quantification: A Variance-Based Perspective
Ruxiao Duan Brian Caffo Harrison X. Bai Haris I. Sair Craig Jones
Uncertainty quantification of deep neural networks has become an active field
of research and plays a crucial role in various downstream tasks such as active
learning. Recent advances in evidential deep learning shed light on the direct
quantification of aleatoric and epistemic uncertainties with a single forward
pass of the model. Most traditional approaches adopt an entropy-based method to
derive evidential uncertainty in classification, quantifying uncertainty at the
sample level. However, the variance-based method that has been widely applied
in regression problems is seldom used in the classification setting. In this
work, we adapt the variance-based approach from regression to classification,
quantifying classification uncertainty at the class level. The variance
decomposition technique in regression is extended to class covariance
decomposition in classification based on the law of total covariance, and the
class correlation is also derived from the covariance. Experiments on
cross-domain datasets are conducted to illustrate that the variance-based
approach not only results in similar accuracy as the entropy-based one in
active domain adaptation but also brings information about class-wise
uncertainties as well as between-class correlations. The code is available at
https://github.com/KerryDRX/EvidentialADA. This alternative means of evidential
uncertainty quantification will give researchers more options when class
uncertainties and correlations are important in their applications.