# Generalized Wasserstein Dice Score, Distributionally Robust Deep Learning, and Ranger for brain tumor segmentation: BraTS 2020 challenge

arXiv: https://arxiv.org/abs/2011.01614 · HTML: https://mlsanity.com/paper/2011.01614/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 7 of 7)

- [Modeling Multimodal Aleatoric Uncertainty in Segmentation with Mixture of Stochastic Experts](https://mlsanity.com/paper/2212.07328/) (2022)
- [Generalized Wasserstein Dice Loss, Test-time Augmentation, and Transformers for the BraTS 2021 challenge](https://mlsanity.com/paper/2112.13054/) (2021)
- [A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentation](https://mlsanity.com/paper/2203.00628/) (2022)
- [Brain Tumor Segmentation Based on Deep Learning, Attention Mechanisms, and Energy-Based Uncertainty Prediction](https://mlsanity.com/paper/2401.00587/) (2023)
- [A novel shape-based loss function for machine learning-based seminal organ segmentation in medical imaging](https://mlsanity.com/paper/2203.03336/) (2022)
- [Two-stage MR Image Segmentation Method for Brain Tumors based on Attention Mechanism](https://mlsanity.com/paper/2304.08072/) (2023)
- [A Novel Global Context-aware Deep Neural Network for Enhanced Brain Tumor Segmentation using Magnetic Resonance Images](https://mlsanity.com/paper/2605.30510/) (2026)

## Abstract (arXiv)

Training a deep neural network is an optimization problem with four main ingredients: the design of the deep neural network, the per-sample loss function, the population loss function, and the optimizer. However, methods developed to compete in recent BraTS challenges tend to focus only on the design of deep neural network architectures, while paying less attention to the three other aspects. In this paper, we experimented with adopting the opposite approach. We stuck to a generic and state-of-the-art 3D U-Net architecture and experimented with a non-standard per-sample loss function, the generalized Wasserstein Dice loss, a non-standard population loss function, corresponding to distributionally robust optimization, and a non-standard optimizer, Ranger. Those variations were selected specifically for the problem of multi-class brain tumor segmentation. The generalized Wasserstein Dice loss is a per-sample loss function that allows taking advantage of the hierarchical structure of the tumor regions labeled in BraTS. Distributionally robust optimization is a generalization of empirical risk minimization that accounts for the presence of underrepresented subdomains in the training dataset. Ranger is a generalization of the widely used Adam optimizer that is more stable with small batch size and noisy labels. We found that each of those variations of the optimization of deep neural networks for brain tumor segmentation leads to improvements in terms of Dice scores and Hausdorff distances. With an ensemble of three deep neural networks trained with various optimization procedures, we achieved promising results on the validation dataset of the BraTS 2020 challenge. Our ensemble ranked fourth out of the 693 registered teams for the segmentation task of the BraTS 2020 challenge.