Finite Sample Bounds for Non-Parametric Regression: Optimal Sample Efficiency and Space Complexity
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911496938717184 |
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| author | Maran, Davide Restelli, Marcello |
| author_facet | Maran, Davide Restelli, Marcello |
| contents | We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional kernel-based estimators often incur high computational costs and memory requirements that scale with the sample size, limiting their utility in real-time applications such as reinforcement learning. To overcome these challenges, we propose a parametric approach based on a finite-dimensional representation that achieves minimax-optimal uniform convergence rates. Our method enables lightweight inference without storing all samples in memory. We provide sharp finite-sample bounds under sub-Gaussian noise, derive second-order Bernstein-type guarantees, and prove matching lower bounds, thereby confirming the optimality of our approach in both estimation error and memory efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Sample Bounds for Non-Parametric Regression: Optimal Sample Efficiency and Space Complexity Maran, Davide Restelli, Marcello Machine Learning We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional kernel-based estimators often incur high computational costs and memory requirements that scale with the sample size, limiting their utility in real-time applications such as reinforcement learning. To overcome these challenges, we propose a parametric approach based on a finite-dimensional representation that achieves minimax-optimal uniform convergence rates. Our method enables lightweight inference without storing all samples in memory. We provide sharp finite-sample bounds under sub-Gaussian noise, derive second-order Bernstein-type guarantees, and prove matching lower bounds, thereby confirming the optimality of our approach in both estimation error and memory efficiency. |
| title | Finite Sample Bounds for Non-Parametric Regression: Optimal Sample Efficiency and Space Complexity |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2412.14744 |