Adaptation using spatially distributed Gaussian Processes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915260110209024 |
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| author | Szabo, Botond Hadji, Amine van der Vaart, Aad |
| author_facet | Szabo, Botond Hadji, Amine van der Vaart, Aad |
| contents | We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that this approximate posterior retains the rate of recovery of the full data posterior distribution, where the rate of recovery adapts to the smoothness of the true regression function. As particular examples we consider Gaussian process priors based on integrated Brownian motion and the Matérn kernel augmented with a prior on the length scale. Besides theoretical guarantees we present a numerical study of the methods both on synthetic and real world data. We also propose a new aggregation technique, which numerically outperforms previous approaches. Finally, we demonstrate empirically that spatially distributed methods can adapt to local regularities, potentially outperforming the original Gaussian process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14130 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adaptation using spatially distributed Gaussian Processes Szabo, Botond Hadji, Amine van der Vaart, Aad Statistics Theory Methodology 62G08, 62G20 We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that this approximate posterior retains the rate of recovery of the full data posterior distribution, where the rate of recovery adapts to the smoothness of the true regression function. As particular examples we consider Gaussian process priors based on integrated Brownian motion and the Matérn kernel augmented with a prior on the length scale. Besides theoretical guarantees we present a numerical study of the methods both on synthetic and real world data. We also propose a new aggregation technique, which numerically outperforms previous approaches. Finally, we demonstrate empirically that spatially distributed methods can adapt to local regularities, potentially outperforming the original Gaussian process. |
| title | Adaptation using spatially distributed Gaussian Processes |
| topic | Statistics Theory Methodology 62G08, 62G20 |
| url | https://arxiv.org/abs/2312.14130 |