Minimax adaptive estimation in manifold inference

DOI10.1214/21-EJS1934zbMath1493.62162arXiv2001.04896MaRDI QIDQ2074315

Vincent Divol

Publication date: 9 February 2022

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.04896

zbMATH Keywords

adaptive estimationgeometric inferenceČech complexmanifold estimation

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (4)

Measure estimation on manifolds: an optimal transport approach ⋮ Adversarial manifold estimation ⋮ Optimal reach estimation and metric learning ⋮ Estimating the reach of a manifold via its convexity defect function

Uses Software

• SciPy
• Python
• IntDim

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local convex hull support and boundary estimation
• Tangent estimation from point samples
• Minimal penalty for Goldenshluger-Lepski method
• Manifold estimation and singular deconvolution under Hausdorff loss
• Tight minimax rates for manifold estimation under Hausdorff loss
• Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications
• Limit properties for ratios of order statistics from exponentials
• Set estimation under convexity type assumptions
• Stability and minimax optimality of tangential Delaunay complexes for manifold reconstruction
• Estimator selection: a new method with applications to kernel density estimation
• Nonasymptotic rates for manifold, tangent space and curvature estimation
• Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
• Estimating the reach of a manifold
• Unconstrained and curvature-constrained shortest-path distances and their approximation
• Manifold reconstruction using tangential Delaunay complexes
• Finding the homology of submanifolds with high confidence from random samples
• Multiscale Dictionary Learning: Non-Asymptotic Bounds and Robustness
• Curvature Measures
• Minimax Rates for Estimating the Dimension of a Manifold
• An adaptive multiclass nearest neighbor classifier
• Minimal penalties and the slope heuristics: a survey
• Minimax Manifold Estimation

This page was built for publication: Minimax adaptive estimation in manifold inference