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

Researchers have developed a minimax lower bound for estimating the finite-scale population functional underlying FLIPD, a diffusion-based local intrinsic dimension (LID) quantity. This quantity is defined by the logarithmic scale derivative of a Gaussian-smoothed density. The study shows that under a regular manifold model, the finite-scale field deviates from the manifold dimension by at most $O(\sigma^2)$. The established minimax lower bound is of order $(n\sigma^d)^{-1}$ for estimating this field from $n$ observations within a specific range of $\sigma$. AI

IMPACT Provides a theoretical foundation for understanding the statistical limitations of diffusion-based methods in analyzing high-dimensional data.

RANK_REASON Academic paper detailing a new theoretical result in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv:2406.03537
• arXiv cs.LG
• Kamkari et al.

• paper
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