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.

预测不确定性估计是一个具有挑战性的问题，阻碍了深度神经网络在安全关键应用中作为子系统的使用。我们通过将不确定性传播视为非线性优化问题，采用因子图的方法，观察到在大部分实验中（包括三个数据集和两种神经网络架构），相较于以前的工作，在性能方面取得了显著的提升。我们的实现平衡了采样和分析传播技术的好处，这在实现性能提升方面起到了关键作用。

使用因子图对经过训练的深度神经网络进行不确定性传播