# GROS: A General Robust Aggregation Strategy

arXiv: https://arxiv.org/abs/2402.15442 · HTML: https://mlsanity.com/paper/2402.15442/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 9 of 9)

- [Sub-Gaussian estimators of the mean of a random vector](https://mlsanity.com/paper/1702.00482/) (2017)
- [A survey on multi-player bandits](https://mlsanity.com/paper/2211.16275/) (2022)
- [A Survey of Online Experiment Design with the Stochastic Multi-Armed Bandit](https://mlsanity.com/paper/1510.00757/) (2015)
- [COBRA: A Combined Regression Strategy](https://mlsanity.com/paper/1303.2236/) (2013)
- [Robust nonparametric regression: review and practical considerations](https://mlsanity.com/paper/2211.08376/) (2022)
- [Set estimation from reflected Brownian motion](https://mlsanity.com/paper/1411.0433/) (2014)
- [Robust Persistence Diagrams using Reproducing Kernels](https://mlsanity.com/paper/2006.10012/) (2020)
- [A nonlinear aggregation type classifier](https://mlsanity.com/paper/1509.01604/) (2015)
- [Adversarially Robust Topological Inference](https://mlsanity.com/paper/2206.01795/) (2022)

## Built on by (most cited first, 1 of 1)

- [Conformal Robust Set Estimation](https://mlsanity.com/paper/2604.18441/) (2026)

## Abstract (arXiv)

A new, very general, robust procedure for combining estimators in metric spaces is introduced GROS. The method is reminiscent of the well-known median of means, as described in citedevroye2016sub. Initially, the sample is divided into K groups. Subsequently, an estimator is computed for each group. Finally, these K estimators are combined using a robust procedure. We prove that this estimator is sub-Gaussian and we get its break-down point, in the sense of Donoho. The robust procedure involves a minimization problem on a general metric space, but we show that the same (up to a constant) sub-Gaussianity is obtained if the minimization is taken over the sample, making GROS feasible in practice. The performance of GROS is evaluated through five simulation studies: the first one focuses on classification using k-means, the second one on the multi-armed bandit problem, the third one on the regression problem. The fourth one is the set estimation problem under a noisy model. Lastly, we apply GROS to get a robust persistent diagram.