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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2602.05225 |
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| _version_ | 1866912880888119296 |
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| author | Györfi, László Humbert, Pierre Bars, Batiste Le |
| author_facet | Györfi, László Humbert, Pierre Bars, Batiste Le |
| contents | We consider the problem of estimating the Fréchet and conditional Fréchet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator that works universally for all metric spaces. Therefore, we introduce a computable estimator for the Fréchet mean based on random quantization techniques and establish its universal consistency across any separable metric spaces. Additionally, we propose another estimator for the conditional Fréchet mean, leveraging data-driven partitioning and quantization, and demonstrate its universal consistency when the output space is any Banach space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Metric space valued Fréchet regression Györfi, László Humbert, Pierre Bars, Batiste Le Statistics Theory Machine Learning We consider the problem of estimating the Fréchet and conditional Fréchet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator that works universally for all metric spaces. Therefore, we introduce a computable estimator for the Fréchet mean based on random quantization techniques and establish its universal consistency across any separable metric spaces. Additionally, we propose another estimator for the conditional Fréchet mean, leveraging data-driven partitioning and quantization, and demonstrate its universal consistency when the output space is any Banach space. |
| title | Metric space valued Fréchet regression |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2602.05225 |