Marginally calibrated response distributions for end-to-end learning in autonomous driving

Abstract

End-to-end learners for autonomous driving are deep neural networks that predict the instantaneous steering angle directly from images of the street ahead. These learners must provide reliable uncertainty estimates for their predictions in order to meet safety requirements and to initiate a switch to manual control in areas of high uncertainty. However, end-to-end learners typically only deliver point predictions, since distributional predictions are associated with large increases in training time or additional computational resources during prediction. To address this shortcoming, we investigate efficient and scalable approximate inference for the deep distributional model of Klein, Nott and Smith (J. Comput. Graph. Statist. 30 (2021) 467–483) in order to quantify uncertainty for the predictions of end-to-end learners. A special merit of this model, which we refer to as implicit copula neural linear model (IC-NLM), is that it produces densities for the steering angle that are marginally calibrated, that is, the average of the estimated densities equals the empirical distribution of steering angles. To ensure the scalability to large n regimes, we develop efficient estimation based on variational inference as a fast alternative to computationally intensive, exact inference via Hamiltonian Monte Carlo. We demonstrate the accuracy and speed of the variational approach on two end-to-end learners trained for highway driving using the comma2k19 dataset. The IC-NLM is competitive with other established uncertainty quantification methods for end-to-end learning in terms of nonprobabilistic predictive performance and outperforms them in terms of marginal calibration for in-distribution prediction. Our proposed approach also allows the identification of overconfident learners and contributes to the explainability of black-box end-to-end learners by using the predictive densities to understand which steering actions the learner sees as valid.