Improved Evidential Deep Learning via a Mixture of Dirichlet
  Distributions
J. Jon Ryu Maohao Shen Soumya Ghosh Yuheng Bu Prasanna Sattigeri Subhro Das Gregory W. Wornell
This paper explores a modern predictive uncertainty estimation approach,
called evidential deep learning (EDL), in which a single neural network model
is trained to learn a meta distribution over the predictive distribution by
minimizing a specific objective function. Despite their strong empirical
performance, recent studies by Bengs et al. identify a fundamental pitfall of
the existing methods: the learned epistemic uncertainty may not vanish even in
the infinite-sample limit. We corroborate the observation by providing a
unifying view of a class of widely used objectives from the literature. Our
analysis reveals that the EDL methods essentially train a meta distribution by
minimizing a certain divergence measure between the distribution and a
sample-size-independent target distribution, resulting in spurious epistemic
uncertainty. Grounded in theoretical principles, we propose learning a
consistent target distribution by modeling it with a mixture of Dirichlet
distributions and learning via variational inference. Afterward, a final meta
distribution model distills the learned uncertainty from the target model.
Experimental results across various uncertainty-based downstream tasks
demonstrate the superiority of our proposed method, and illustrate the
practical implications arising from the consistency and inconsistency of
learned epistemic uncertainty.