Predictive Uncertainty Quantification with Compound Density Networks
This work addresses uncertainty quantification for deep learning practitioners, offering incremental improvements over existing Bayesian and ensemble approaches.
The paper tackles the problem of quantifying prediction uncertainty in deep neural networks by introducing compound density networks (CDNs), which improve uncertainty estimates on out-of-distribution data and robustness to adversarial examples compared to prior methods.
Despite the huge success of deep neural networks (NNs), finding good mechanisms for quantifying their prediction uncertainty is still an open problem. Bayesian neural networks are one of the most popular approaches to uncertainty quantification. On the other hand, it was recently shown that ensembles of NNs, which belong to the class of mixture models, can be used to quantify prediction uncertainty. In this paper, we build upon these two approaches. First, we increase the mixture model's flexibility by replacing the fixed mixing weights by an adaptive, input-dependent distribution (specifying the probability of each component) represented by NNs, and by considering uncountably many mixture components. The resulting class of models can be seen as the continuous counterpart to mixture density networks and is therefore referred to as compound density networks (CDNs). We employ both maximum likelihood and variational Bayesian inference to train CDNs, and empirically show that they yield better uncertainty estimates on out-of-distribution data and are more robust to adversarial examples than the previous approaches.