On the distance between mean and geometric median in high dimensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918343863173120 |
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| author | Schwank, Richard Drton, Mathias |
| author_facet | Schwank, Richard Drton, Mathias |
| contents | The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion of the geometric median components. Simulations illustrate and confirm our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the distance between mean and geometric median in high dimensions Schwank, Richard Drton, Mathias Statistics Theory Probability Machine Learning The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion of the geometric median components. Simulations illustrate and confirm our results. |
| title | On the distance between mean and geometric median in high dimensions |
| topic | Statistics Theory Probability Machine Learning |
| url | https://arxiv.org/abs/2508.12926 |