Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks

TL;DR

This paper introduces hinge-Wasserstein, a novel loss function for regression tasks that improves multimodal uncertainty estimation in computer vision by better modeling complex probability distributions without full ground truth.

Contribution

The paper proposes hinge-Wasserstein, an improved loss function for regression-by-classification that enhances multimodal distribution modeling and uncertainty estimation without requiring complete ground truth distributions.

Findings

Hinge-Wasserstein reduces overconfidence in probability estimates.

The method improves uncertainty quantification in horizon line detection.

Enhanced distribution modeling in stereo disparity estimation.

Abstract

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.