Uncertainty quantification and out-of-distribution detection using
  surjective normalizing flows
Simon Dirmeier Ye Hong Yanan Xin Fernando Perez-Cruz
Reliable quantification of epistemic and aleatoric uncertainty is of crucial
importance in applications where models are trained in one environment but
applied to multiple different environments, often seen in real-world
applications for example, in climate science or mobility analysis. We propose a
simple approach using surjective normalizing flows to identify
out-of-distribution data sets in deep neural network models that can be
computed in a single forward pass. The method builds on recent developments in
deep uncertainty quantification and generative modeling with normalizing flows.
We apply our method to a synthetic data set that has been simulated using a
mechanistic model from the mobility literature and several data sets simulated
from interventional distributions induced by soft and atomic interventions on
that model, and demonstrate that our method can reliably discern
out-of-distribution data from in-distribution data. We compare the surjective
flow model to a Dirichlet process mixture model and a bijective flow and find
that the surjections are a crucial component to reliably distinguish
in-distribution from out-of-distribution data.