Bayesian neural networks uncertainty quantification with cubature rules

Bayesian neural networks are powerful inference methods by accounting for randomness in the data and the network model. Uncertainty quantification at the output of neural networks is critical, especially for applications such as autonomous driving and hazardous weather forecasting. However, approaches for theoretical analysis of Bayesian neural networks remain limited. This paper makes a step forward towards mathematical quantification of uncertainty in neural network models and proposes a cubature-rule-based computationally-efficient uncertainty quantification approach that captures layer-wise uncertainties of Bayesian neural networks. The proposed approach approximates the first two moments of the posterior distribution of the parameters by propagating cubature points across the network nonlinearities. Simulation results show that the proposed approach can achieve more diverse layer-wise uncertainty quantification results of neural networks with a fast convergence rate.