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Concentration bounds for intrinsic dimension estimation using Gaussian kernels

arXiv 2512.04861 ↗First posted 4 Dec 2025math.ST stat.ML stat.THcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 5 of its 25 references that are in the map. First posted on arXiv 4 Dec 2025.

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References · 5

  1. 2019Intrinsic dimension of data representations in deep neural networkscited by 282
  2. 2018Estimating the intrinsic dimension of datasets by a minimal neighborhood informationcited by 250
  3. 2021Intrinsic Dimension, Persistent Homology and Generalization in Neural Networkscited by 70
  4. 2023Generalization Bounds with Data-dependent Fractal Dimensionscited by 15
  5. 2025A Survey of Dimension Estimation Methodscited by 12

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