In recent years, there has been increased interest in the design, training, and evaluation of end-to-end autonomous driving (AD) systems. One often overlooked aspect is the uncertainty of planned trajectories predicted by these systems, despite awareness of their own uncertainty being key to achieve safety and robustness. We propose to estimate this uncertainty by adapting loss prediction from the uncertainty quantification literature. To this end, we introduce a novel light-weight module, dubbed CATPlan, that is trained to decode motion and planning embeddings into estimates of the collision loss used to partially supervise end-to-end AD systems. During inference, these estimates are interpreted as collision risk. We evaluate CATPlan on the safety-critical, nerf-based, closed-loop benchmark NeuroNCAP and find that it manages to detect collisions with a $54.8\%$ relative improvement to average precision over a GMM-based baseline in which the predicted trajectory is compared to the forecasted trajectories of other road users. Our findings indicate that the addition of CATPlan can lead to safer end-to-end AD systems and hope that our work will spark increased interest in uncertainty quantification for such systems.

Computer vision systems that are deployed in safety-critical applications need to quantify their output uncertainty. We study regression from images to parameter values and here it is common to detect uncertainty by predicting probability distributions. In this context, we investigate the regression-by-classification paradigm which can represent multimodal distributions, without a prior assumption on the number of modes. Through experiments on a specifically designed synthetic dataset, we demonstrate that traditional loss functions lead to poor probability distribution estimates and severe overconfidence, in the absence of full ground truth distributions. In order to alleviate these issues, we propose hinge-Wasserstein -- a simple improvement of the Wasserstein loss that reduces the penalty for weak secondary modes during training. This enables prediction of complex distributions with multiple modes, and allows training on datasets where full ground truth distributions are not available. In extensive experiments, we show that the proposed loss leads to substantially better uncertainty estimation on two challenging computer vision tasks: horizon line detection and stereo disparity estimation.