Deconvolution for the Wasserstein metric and geometric inference

DOI10.1214/11-EJS646zbMath1274.62363MaRDI QIDQ1952230

Bertrand Michel, Claire Caillerie, Fréderic Chazal, Jérôme Dedecker

Publication date: 28 May 2013

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

Full work available at URL: https://projecteuclid.org/euclid.ejs/1320416979

zbMATH Keywords

deconvolutionWasserstein distancegeometric inferencecomputational topology

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Spaces of measures, convergence of measures (28A33) Convergence of probability measures (60B10)

Related Items (12)

Entropic optimal transport is maximum-likelihood deconvolution ⋮ Rates of convergence for robust geometric inference ⋮ Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension ⋮ Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces ⋮ Minimax rate of distribution estimation on unknown submanifolds under adversarial losses ⋮ Manifold estimation and singular deconvolution under Hausdorff loss ⋮ Nonparametric ridge estimation ⋮ Robust Topological Inference: Distance To a Measure and Kernel Distance ⋮ A parametric registration model for warped distributions with Wasserstein's distance ⋮ Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one ⋮ Minimax estimation of smooth optimal transport maps ⋮ From Empirical Observations to Tree Models for Stochastic Optimization: Convergence Properties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric inference for probability measures
• Consistent density deconvolution under partially known error distribution
• Deconvolution problems in nonparametric statistics
• Exact rates in density support estimation
• A sampling theory for compact sets in Euclidean space
• On the path density of a gradient field
• Nonparametric estimation of the measurement error model using multiple indicators.
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model
• Empirical geometry of multivariate data: a deconvolution approach.
• Mean rates of convergence of empirical measures in the Wasserstein metric
• Deconvolving compactly supported densities
• Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees
• On optimal kernel choice for deconvolution
• Estimating the support of multivariate densities under measurement error
• A nonparametric approach to the estimation of lengths and surface areas
• On some expansions of stable distribution functions
• A Topological View of Unsupervised Learning from Noisy Data
• Data-Driven Density Estimation in the Presence of Additive Noise with unknown Distribution
• Support estimation via moment estimation in presence of noise
• Deconvolving kernel density estimators
• Semiconcave functions in Alexandrov's geometry
• Optimal Rates of Convergence for Deconvolving a Density
• On the effect of estimating the error density in nonparametric deconvolution
• Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error
• Estimating the number of clusters
• On the effect of misspecifying the error density in a deconvolution problem
• Consistent deconvolution in density estimation
• Principal Curves
• The Geometry of Nonparametric Filament Estimation
• Optimal Transport

This page was built for publication: Deconvolution for the Wasserstein metric and geometric inference