  Quantification of uncertainty is one of the most promising approaches to
establish safe machine learning. Despite its importance, it is far from being
generally solved, especially for neural networks. One of the most commonly used
approaches so far is Monte Carlo dropout, which is computationally cheap and
easy to apply in practice. However, it can underestimate the uncertainty. We
propose a new objective, referred to as second-moment loss (SML), to address
this issue. While the full network is encouraged to model the mean, the dropout
networks are explicitly used to optimize the model variance. We intensively
study the performance of the new objective on various UCI regression datasets.
Comparing to the state-of-the-art of deep ensembles, SML leads to comparable
prediction accuracies and uncertainty estimates while only requiring a single
model. Under distribution shift, we observe moderate improvements. As a side
result, we introduce an intuitive Wasserstein distance-based uncertainty
measure that is non-saturating and thus allows to resolve quality differences
between any two uncertainty estimates.
