Estimating Multimodal Aleatoric Uncertainty in Regression Tasks Using Hinge-Wasserstein Loss

Core Concepts

The authors propose the hinge-Wasserstein loss, a simple improvement to the Wasserstein loss, to better estimate multimodal aleatoric uncertainty in regression tasks when full ground truth distributions are unavailable.

Abstract

The authors study regression from images to parameter values, where the output uncertainty is often multimodal due to factors like occlusions and low-resolution measurements. They investigate the regression-by-classification paradigm, which can represent multimodal distributions without a prior assumption on the number of modes. Through experiments on a synthetic dataset, the authors demonstrate that traditional loss functions like L1 and L2 lead to poor probability distribution estimates and severe overconfidence when full ground truth distributions are not available. To address this issue, the authors propose the hinge-Wasserstein loss, which reduces the penalty for weak secondary modes during training. This enables the prediction of complex distributions with multiple modes and allows training on datasets where full ground truth distributions are not available. The authors show that the hinge-Wasserstein loss leads to substantially better uncertainty estimation on two challenging computer vision tasks: horizon line detection and stereo disparity estimation. Compared to the plain Wasserstein loss, the hinge-Wasserstein loss significantly improves uncertainty estimation while maintaining the main task performance, especially under multimodal aleatoric uncertainty.

Stats

Observations in many regression tasks are subject to aleatoric uncertainty, which cannot be reduced even with more data. Boundary pixels in stereo disparity estimation often have a high likelihood of both the foreground and the background, leading to multimodal distributions. The mean of the predicted distribution can deviate from the most likely mode, which is usually the desired prediction.

Quotes

"In the multimodal case as shown in Fig. 1, the mean can deviate from the most likely mode (which is usually the desired prediction) and is instead located in a region of low likelihood." "To the best of our knowledge, none of the previous RbC works consider aleatoric uncertainty estimation in scenarios where multimodal ground truth distributions are unavailable."

Key Insights Distilled From

Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks

by Ziliang Xion... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2306.00560.pdf

Deeper Inquiries

How can the hinge-Wasserstein loss be extended to handle higher-dimensional regression tasks with multimodal aleatoric uncertainty

To extend the hinge-Wasserstein loss for higher-dimensional regression tasks with multimodal aleatoric uncertainty, we can modify the loss function to handle multiple output dimensions. In the context of computer vision tasks like depth estimation or object pose estimation, where the regression space is partitioned into bins, we can generalize the hinge-Wasserstein loss to work with multiple output dimensions. This can be achieved by adapting the loss calculation to consider the multimodal distributions in each output dimension separately. By incorporating the principles of regression-by-classification for each dimension, we can ensure that the model captures the uncertainty associated with each dimension independently. Additionally, the hinge mechanism can be applied to each dimension to allow for the representation of multiple modes in the predicted distributions. This extension would enable the model to effectively estimate uncertainty in higher-dimensional regression tasks by considering the multimodal nature of the output distributions across all dimensions.

What are the potential drawbacks or limitations of the regression-by-classification approach, and how can they be addressed

One potential drawback of the regression-by-classification approach is the assumption of discretizing the continuous target variables into bins, which may introduce quantization errors and limit the resolution of the predictions. This discretization can lead to information loss and may not fully capture the continuous nature of the output space. To address this limitation, techniques such as using a larger number of bins or implementing a more sophisticated decoding mechanism can help improve the resolution of the predictions and reduce quantization errors. Additionally, the reliance on softmax normalization in the final layer may restrict the model's ability to represent complex multimodal distributions. By exploring alternative normalization techniques, such as softplus followed by L1 normalization, the model can better capture the uncertainty associated with multimodal distributions. Furthermore, incorporating ensemble methods or Bayesian approaches can enhance the model's ability to quantify uncertainty and improve the robustness of the predictions.

How can the insights from this work on multimodal aleatoric uncertainty estimation be applied to other domains beyond computer vision, such as robotics or finance

The insights gained from this work on multimodal aleatoric uncertainty estimation in regression tasks can be applied to various domains beyond computer vision, such as robotics and finance. In robotics, where sensor data often exhibit inherent uncertainty, the regression-by-classification paradigm can be utilized to model and quantify this uncertainty in tasks like localization, mapping, and object manipulation. By training models with the hinge-Wasserstein loss, robotic systems can make more informed decisions based on probabilistic predictions that account for multimodal distributions. In finance, where predicting market trends and risk assessment are crucial, the ability to estimate uncertainty in regression tasks can enhance decision-making processes. By leveraging the principles of uncertainty quantification learned from this research, financial models can provide more reliable predictions and risk assessments, leading to better investment strategies and portfolio management. Overall, the techniques and methodologies developed for handling multimodal aleatoric uncertainty in regression tasks have broad applications across various domains, offering valuable insights for improving predictive modeling and decision support systems.