Concentration bounds for intrinsic dimension estimation using Gaussian kernels
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914343050805248 |
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| author | Andersson, Martin |
| author_facet | Andersson, Martin |
| contents | We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters, characterizing precisely how regularity conditions influence statistical performance. We also propose a bandwidth selection heuristic using derivative information, supported by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration bounds for intrinsic dimension estimation using Gaussian kernels Andersson, Martin Statistics Theory Machine Learning 62R30 (Primary), 60E15 (Secondary) We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters, characterizing precisely how regularity conditions influence statistical performance. We also propose a bandwidth selection heuristic using derivative information, supported by numerical experiments. |
| title | Concentration bounds for intrinsic dimension estimation using Gaussian kernels |
| topic | Statistics Theory Machine Learning 62R30 (Primary), 60E15 (Secondary) |
| url | https://arxiv.org/abs/2512.04861 |