Uncertainty Propagation through Trained Deep Neural Networks Using
  Factor Graphs
Angel Daruna Yunye Gong Abhinav Rajvanshi Han-Pang Chiu Yi Yao
Predictive uncertainty estimation remains a challenging problem precluding
the use of deep neural networks as subsystems within safety-critical
applications. Aleatoric uncertainty is a component of predictive uncertainty
that cannot be reduced through model improvements. Uncertainty propagation
seeks to estimate aleatoric uncertainty by propagating input uncertainties to
network predictions. Existing uncertainty propagation techniques use one-way
information flows, propagating uncertainties layer-by-layer or across the
entire neural network while relying either on sampling or analytical techniques
for propagation. Motivated by the complex information flows within deep neural
networks (e.g. skip connections), we developed and evaluated a novel approach
by posing uncertainty propagation as a non-linear optimization problem using
factor graphs. We observed statistically significant improvements in
performance over prior work when using factor graphs across most of our
experiments that included three datasets and two neural network architectures.
Our implementation balances the benefits of sampling and analytical propagation
techniques, which we believe, is a key factor in achieving performance
improvements.