# Distributionally Robust Deep Learning using Hardness Weighted Sampling

arXiv: https://arxiv.org/abs/2001.02658 · HTML: https://mlsanity.com/paper/2001.02658/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [Taxonomy of Machine Learning Safety: A Survey and Primer](https://mlsanity.com/paper/2106.04823/) (2021)
- [A Dempster-Shafer approach to trustworthy AI with application to fetal brain MRI segmentation](https://mlsanity.com/paper/2204.02779/) (2022)
- [Distributionally Robust Segmentation of Abnormal Fetal Brain 3D MRI](https://mlsanity.com/paper/2108.04175/) (2021)
- [Stochastic Re-weighted Gradient Descent via Distributionally Robust Optimization](https://mlsanity.com/paper/2306.09222/) (2023)

## Abstract (arXiv)

Limiting failures of machine learning systems is of paramount importance for safety-critical applications. In order to improve the robustness of machine learning systems, Distributionally Robust Optimization (DRO) has been proposed as a generalization of Empirical Risk Minimization (ERM). However, its use in deep learning has been severely restricted due to the relative inefficiency of the optimizers available for DRO in comparison to the wide-spread variants of Stochastic Gradient Descent (SGD) optimizers for ERM. We propose SGD with hardness weighted sampling, a principled and efficient optimization method for DRO in machine learning that is particularly suited in the context of deep learning. Similar to a hard example mining strategy in practice, the proposed algorithm is straightforward to implement and computationally as efficient as SGD-based optimizers used for deep learning, requiring minimal overhead computation. In contrast to typical ad hoc hard mining approaches, we prove the convergence of our DRO algorithm for over-parameterized deep learning networks with ReLU activation and a finite number of layers and parameters. Our experiments on fetal brain 3D MRI segmentation and brain tumor segmentation in MRI demonstrate the feasibility and the usefulness of our approach. Using our hardness weighted sampling for training a state-of-the-art deep learning pipeline leads to improved robustness to anatomical variabilities in automatic fetal brain 3D MRI segmentation using deep learning and to improved robustness to the image protocol variations in brain tumor segmentation. Our code is available at https://github.com/LucasFidon/HardnessWeightedSampler.