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Research questionWhat are the fundamental sample-size limits for estimating diffusion-based local intrinsic dimension at finite smoothing scales?Gaussian smoothing turns local geometry into a scale-dependent functional, but finite samples make that functional difficult to estimate, especially as the smoothing scale becomes small. The target is defined through the logarithmic scale derivative of a Gaussian-smoothed density.
Machine Learning
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Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic DimensionThe source studies the finite-scale field underlying FLIPD from n observations. It reports a uniform O(σ²) difference between this field and the manifold dimension, plus a minimax lower bound of order (nσ^d)^−1 for n^−1/(2α+d) ≲ σ ≤ σ₀; at the smallest covered scale, this becomes n^−2α/(2α+d). The evidence is limited to the stated regular-manifold model and lower-bound analysis.research paper · Sep 4, 2026
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