Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimension
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 population functional underlying FLIPD (Kamkari et al., 2024; arXiv:2406.03537), a diffusion-based local intrinsic dimension (LID) quantity defined through the logarithmic scale derivative of a Gaussian-smoothed density. Intuitively, Gaussian smoothing turns local dimension into a scale law: near a $d$-dimensional manifold, the kernel mass grows like $σ^d$, so differentiating with respect to the noise scale reveals the intrinsic exponent. Under a regular manifold ...
| Authors | Jaehee Seo, Wontae Jeong, Jisu Kim |
|---|---|
| Primary category | stat.ML |
| Published | 4 September 2026 |
| Last updated at source | 4 September 2026 |
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