# Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks

arXiv: https://arxiv.org/abs/2306.00560 · HTML: https://mlsanity.com/paper/2306.00560/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [End-to-End Learning of Geometry and Context for Deep Stereo Regression](https://mlsanity.com/paper/1703.04309/) (2017)
- [Deep multi-scale video prediction beyond mean square error](https://mlsanity.com/paper/1511.05440/) (2015)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Bounding Box Regression with Uncertainty for Accurate Object Detection](https://mlsanity.com/paper/1809.08545/) (2018)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Neural-Guided RANSAC: Learning Where to Sample Model Hypotheses](https://mlsanity.com/paper/1905.04132/) (2019)
- [Wasserstein Distances for Stereo Disparity Estimation](https://mlsanity.com/paper/2007.03085/) (2020)
- [Horizon Lines in the Wild](https://mlsanity.com/paper/1604.02129/) (2016)
- [Conservative Wasserstein Training for Pose Estimation](https://mlsanity.com/paper/1911.00962/) (2019)
- [Using proper divergence functions to evaluate climate models](https://mlsanity.com/paper/1301.5927/) (2013)
- [Object Detection as Probabilistic Set Prediction](https://mlsanity.com/paper/2203.07980/) (2022)
- [Uncertainty Estimation in Deep Speech Enhancement Using Complex Gaussian Mixture Models](https://mlsanity.com/paper/2212.04831/) (2022)

## Built on by (most cited first, 1 of 1)

- [FACT: Multinomial Misalignment Classification for Point Cloud Registration](https://mlsanity.com/paper/2504.06627/) (2025)

## Abstract (arXiv)

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.