GROS: A General Robust Aggregation Strategy
Abstract
A new, very general, robust procedure for combining estimators in metric spaces is introduced GROS. The method is reminiscent of the wellknown median of means, as described in \cite{devroye2016sub}. 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 subGaussian and we get its breakdown 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) subGaussianity 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 multiarmed 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.15442
 arXiv:
 arXiv:2402.15442
 Bibcode:
 2024arXiv240215442C
 Keywords:

 Mathematics  Statistics Theory;
 Statistics  Applications;
 Statistics  Machine Learning