GROS: A General Robust Aggregation Strategy
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911783005978624 |
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| author | Cholaquidis, Alejandro Joly, Emilien Moreno, Leonardo |
| author_facet | Cholaquidis, Alejandro Joly, Emilien Moreno, Leonardo |
| contents | 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 \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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GROS: A General Robust Aggregation Strategy Cholaquidis, Alejandro Joly, Emilien Moreno, Leonardo Statistics Theory Applications Machine Learning 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 \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 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. |
| title | GROS: A General Robust Aggregation Strategy |
| topic | Statistics Theory Applications Machine Learning |
| url | https://arxiv.org/abs/2402.15442 |