Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence
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_ | 1866917629715808256 |
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| author | Leluc, Rémi Portier, François Segers, Johan Zhuman, Aigerim |
| author_facet | Leluc, Rémi Portier, François Segers, Johan Zhuman, Aigerim |
| contents | A novel linear integration rule called $\textit{control neighbors}$ is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure on metric spaces. The main result is the $\mathcal{O}(n^{-1/2} n^{-s/d})$ convergence rate -- where $n$ stands for the number of evaluations of the integrand and $d$ for the dimension of the domain -- of this estimate for Hölder functions with regularity $s \in (0,1]$, a rate which, in some sense, is optimal. Several numerical experiments validate the complexity bound and highlight the good performance of the proposed estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06151 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence Leluc, Rémi Portier, François Segers, Johan Zhuman, Aigerim Numerical Analysis Statistics Theory Computation A novel linear integration rule called $\textit{control neighbors}$ is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure on metric spaces. The main result is the $\mathcal{O}(n^{-1/2} n^{-s/d})$ convergence rate -- where $n$ stands for the number of evaluations of the integrand and $d$ for the dimension of the domain -- of this estimate for Hölder functions with regularity $s \in (0,1]$, a rate which, in some sense, is optimal. Several numerical experiments validate the complexity bound and highlight the good performance of the proposed estimator. |
| title | Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence |
| topic | Numerical Analysis Statistics Theory Computation |
| url | https://arxiv.org/abs/2305.06151 |