# Distributionally Robust Multiclass Classification and Applications in Deep Image Classifiers

arXiv: https://arxiv.org/abs/2109.12772 · HTML: https://mlsanity.com/paper/2109.12772/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [A study of the effect of JPG compression on adversarial images](https://mlsanity.com/paper/1608.00853/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Wasserstein Distributionally Robust Optimization and Variation Regularization](https://mlsanity.com/paper/1712.06050/) (2017)

## Built on by (most cited first, 3 of 3)

- [Wasserstein Distributionally Robust Multiclass Support Vector Machine](https://mlsanity.com/paper/2409.08409/) (2024)
- [Distributionally Robust Learning in Survival Analysis](https://mlsanity.com/paper/2506.01348/) (2025)
- [Improving Mixup Calibration with Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2506.17874/) (2025)

## Abstract (arXiv)

We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of distributions that are close to the empirical distribution of the training set in the sense of the Wasserstein metric. We relax the DRO formulation into a regularized learning problem whose regularizer is a norm of the coefficient matrix. We establish out-of-sample performance guarantees for the solutions to our model, offering insights on the role of the regularizer in controlling the prediction error. We apply the proposed method in rendering deep Vision Transformer (ViT)-based image classifiers robust to random and adversarial attacks. Specifically, using the MNIST and CIFAR-10 datasets, we demonstrate reductions in test error rate by up to 83.5% and loss by up to 91.3% compared with baseline methods, by adopting a novel random training method.