Robust Online Sampling from Possibly Moving Target Distributions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908589712474112 |
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| author | Clément, François Steinerberger, Stefan |
| author_facet | Clément, François Steinerberger, Stefan |
| contents | We suppose we are given a list of points $x_1, \dots, x_n \in \mathbb{R}$, a target probability measure $μ$ and are asked to add additional points $x_{n+1}, \dots, x_{n+m}$ so that $x_1, \dots, x_{n+m}$ is as close as possible to the distribution of $μ$; additionally, we want this to be true uniformly for all $m$. We propose a simple method that achieves this goal. It selects new points in regions where the existing set is lacking points and avoids regions that are already overly crowded. If we replace $μ$ by another measure $μ_2$ in the middle of the computation, the method dynamically adjusts and allows us to keep the original sampling points. $x_{n+1}$ can be computed in $\mathcal{O}(n)$ steps and we obtain state-of-the-art results. It appears to be an interesting dynamical system in its own right; we analyze a continuous mean-field version that reflects much of the same behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Online Sampling from Possibly Moving Target Distributions Clément, François Steinerberger, Stefan Optimization and Control Data Structures and Algorithms Statistics Theory We suppose we are given a list of points $x_1, \dots, x_n \in \mathbb{R}$, a target probability measure $μ$ and are asked to add additional points $x_{n+1}, \dots, x_{n+m}$ so that $x_1, \dots, x_{n+m}$ is as close as possible to the distribution of $μ$; additionally, we want this to be true uniformly for all $m$. We propose a simple method that achieves this goal. It selects new points in regions where the existing set is lacking points and avoids regions that are already overly crowded. If we replace $μ$ by another measure $μ_2$ in the middle of the computation, the method dynamically adjusts and allows us to keep the original sampling points. $x_{n+1}$ can be computed in $\mathcal{O}(n)$ steps and we obtain state-of-the-art results. It appears to be an interesting dynamical system in its own right; we analyze a continuous mean-field version that reflects much of the same behavior. |
| title | Robust Online Sampling from Possibly Moving Target Distributions |
| topic | Optimization and Control Data Structures and Algorithms Statistics Theory |
| url | https://arxiv.org/abs/2510.11571 |