# Distributionally Robust Multi-Output Regression Ranking

arXiv: https://arxiv.org/abs/2109.12803 · HTML: https://mlsanity.com/paper/2109.12803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 27 Sep 2021.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Secure and Robust Machine Learning for Healthcare: A Survey](https://mlsanity.com/paper/2001.08103/) (2020)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [A Survey of Black-Box Adversarial Attacks on Computer Vision Models](https://mlsanity.com/paper/1912.01667/) (2019)
- [Wasserstein Distributionally Robust Optimization and Variation Regularization](https://mlsanity.com/paper/1712.06050/) (2017)
- [An Alternative Cross Entropy Loss for Learning-to-Rank](https://mlsanity.com/paper/1911.09798/) (2019)
- [GPU-acceleration for Large-scale Tree Boosting](https://mlsanity.com/paper/1706.08359/) (2017)
- [A Communication-Efficient Parallel Algorithm for Decision Tree](https://mlsanity.com/paper/1611.01276/) (2016)
- [Robustified Multivariate Regression and Classification Using Distributionally Robust Optimization under the Wasserstein Metric](https://mlsanity.com/paper/2006.06090/) (2020)

## Abstract (arXiv)

Despite their empirical success, most existing listwiselearning-to-rank (LTR) models are not built to be robust to errors in labeling or annotation, distributional data shift, or adversarial data perturbations. To fill this gap, we introduce a new listwise LTR model called Distributionally Robust Multi-output Regression Ranking (DRMRR). Different from existing methods, the scoring function of DRMRR was designed as a multivariate mapping from a feature vector to a vector of deviation scores, which captures local context information and cross-document interactions. DRMRR uses a Distributionally Robust Optimization (DRO) framework to minimize a multi-output loss function under the most adverse distributions in the neighborhood of the empirical data distribution defined by a Wasserstein ball. We show that this is equivalent to a regularized regression problem with a matrix norm regularizer. Our experiments were conducted on two real-world applications, medical document retrieval, and drug response prediction, showing that DRMRR notably outperforms state-of-the-art LTR models. We also conducted a comprehensive analysis to assess the resilience of DRMRR against various types of noise: Gaussian noise, adversarial perturbations, and label poisoning. We show that DRMRR is not only able to achieve significantly better performance than other baselines, but it can maintain a relatively stable performance as more noise is added to the data.