Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks

Ziliang Xiong, Arvi Jonnarth, Abdelrahman Eldesokey, Joakim Johnander, Bastian Wandt, Per-Erik Forssén; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2024, pp. 3471-3480

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.