SEP 4, 2026 · PREPRINT
Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimension
arXiv
This is a theoretical analysis establishing minimax lower bounds for a statistical estimation problem; it raises and partially answers a question about statistical difficulty but does not empirically validate the practical utility or achievability of these bounds.
Reported
Finite-scale field approximation…O(σ²)
Minimax lower bound (general regi…(nσ^d)^{-1}
Minimax lower bound (smallest sca…n^{-2α/(2α+d)}