Concentration bounds for intrinsic dimension estimation using Gaussian kernels

• URL: http://arxiv.org/abs/2512.04861v1
• Date: Thu, 04 Dec 2025 14:45:08 GMT
• Title: Concentration bounds for intrinsic dimension estimation using Gaussian kernels
• Authors: Martin Andersson,
• Abstract summary: We prove finite-sample concentration and anti-concentration bounds for dimension estimation.<n>Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters.<n>We also propose a bandwidth selection using derivative information, which shows promise in numerical experiments.
• Score: 1.157423546614283
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 govern statistical performance. We also propose a bandwidth selection heuristic using derivative information, which shows promise in numerical experiments.

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