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Predictive uncertainty estimation remains a challenging problem precludingthe use of deep neural networks as subsystems within safety-criticalapplications. Aleatoric uncertainty is a component of predictive uncertaintythat cannot be reduced through model improvements. Uncertainty propagationseeks to estimate aleatoric uncertainty by propagating input uncertainties tonetwork predictions. Existing uncertainty propagation techniques use one-wayinformation flows, propagating uncertainties layer-by-layer or across theentire neural network while relying either on sampling or analytical techniquesfor propagation. Motivated by the complex information flows within deep neuralnetworks (e.g. skip connections), we developed and evaluated a novel approachby posing uncertainty propagation as a non-linear optimization problem usingfactor graphs. We observed statistically significant improvements inperformance over prior work when using factor graphs across most of ourexperiments that included three datasets and two neural network architectures.Our implementation balances the benefits of sampling and analytical propagationtechniques, which we believe, is a key factor in achieving performanceimprovements.

Uncertainty Propagation through Trained Deep Neural Networks Using Factor Graphs