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New minimax lower bound established for diffusion-based local intrinsic dimension estimation

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员为估计FLIPD（一种基于扩散的局部内在维度（LID）量）的有限尺度总体函数开发了一个minimax下界。该量由高斯平滑密度的对数尺度导数定义。研究表明，在正则流形模型下，有限尺度场与流形维数的偏差最多为 $O(\sigma^2)$。所建立的minimax下界在从特定范围 $\sigma$ 内的 $n$ 个观测值估计该场时，其阶数为 $(n\sigma^d)^{-1}$。 AI

影响 为理解基于扩散的方法在分析高维数据时的统计局限性提供了理论基础。

排序理由 学术论文，详细介绍了机器学习中的一项新理论成果。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

AI 生成摘要 · Google Gemini · 来自 1 个来源。 我们如何撰写摘要 →

New minimax lower bound established for diffusion-based local intrinsic dimension estimation

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学术论文，详细介绍了机器学习中的一项新理论成果。[lever_c_demoted from research: ic=1 ai=1.0]
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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Jaehee Seo, Wontae Jeong, Jisu Kim ·

    Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimension

    arXiv:2609.04822v1 Announce Type: cross Abstract: While diffusion-based methods have recently emerged as effective tools for probing the intrinsic geometry of high-dimensional data, their statistical difficulty remains largely unexplored. We study estimation of the finite-scale p…

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