4.2 Review

Projection-based techniques for high-dimensional optimal transport problems

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Computer Science, Artificial Intelligence

Representing Graphs via Gromov-Wasserstein Factorization

Hongteng Xu et al.

Summary: Gromov-Wasserstein Factorization (GWF) is a novel paradigm for learning graph representations. It reconstructs graphs by combining graph factors using a pseudo-metric called Gromov-Wasserstein discrepancy. The shared graph factors represent typical patterns of the graphs' structures.

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (2023)

Article Statistics & Probability

Model-Free Feature Screening and FDR Control With Knockoff Features

Wanjun Liu et al.

Summary: This article proposes a model-free and data-adaptive feature screening method based on projection correlation for ultrahigh-dimensional data. It enjoys sure screening and rank consistency properties and can be applied to data with heavy tails and multivariate responses. A two-step approach with knockoff features is advocated to control the false discovery rate (FDR) under a prespecified level. The proposed method demonstrates superior empirical performance through simulation examples and real data applications.

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (2022)

Article Statistics & Probability

Smoothing Splines Approximation Using Hilbert Curve Basis Selection

Cheng Meng et al.

Summary: Smoothing splines are commonly used in nonparametric regressions, but their computational burden is significant for large sample sizes. Basis selection methods approximate smoothing spline estimators with fewer basis functions, but often assume uniform sample distribution on a hypercube. We propose an efficient algorithm adaptive to the unknown probability density function of predictors to overcome this limitation.

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS (2022)

Article Statistics & Probability

MINIMAX ESTIMATION OF SMOOTH OPTIMAL TRANSPORT MAPS

Jan-Christian Huetter et al.

Summary: The Brenier's theorem establishes the existence of an optimal transport map T between two probability distributions under certain regularity conditions. This work aims to establish minimax estimation rates for such a transport map from data sampled from the distributions under smoothness assumptions on T. By developing an estimator based on empirical versions of the semidual optimal transport problem and providing numerical experiments supporting the theoretical findings, the study demonstrates the practical benefits of smoothness regularization in achieving near minimax optimality for transport maps in general dimension.

ANNALS OF STATISTICS (2021)

Article Statistics & Probability

STATISTICAL INFERENCE FOR BURES-WASSERSTEIN BARYCENTERS

Alexey Kroshnin et al.

Summary: In this work, the concept of Bures-Wasserstein barycenter Q(*) is introduced, with conditions ensuring its existence and uniqueness discussed, as well as its application in statistical inference in quantum mechanics explored.

ANNALS OF APPLIED PROBABILITY (2021)

Article Mathematics, Applied

Empirical Regularized Optimal Transport: Statistical Theory and Applications

Marcel Klatt et al.

SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE (2020)

Proceedings Paper Computer Science, Artificial Intelligence

FlipTest: Fairness Testing via Optimal Transport

Emily Black et al.

FAT* '20: PROCEEDINGS OF THE 2020 CONFERENCE ON FAIRNESS, ACCOUNTABILITY, AND TRANSPARENCY (2020)

Article Biochemical Research Methods

optimalFlow: optimal transport approach to flow cytometry gating and population matching

Eustasio del Barrio et al.

BMC BIOINFORMATICS (2020)

Article Engineering, Electrical & Electronic

CycleGAN With a Blur Kernel for Deconvolution Microscopy: Optimal Transport Geometry

Sungjun Lim et al.

IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING (2020)

Article Statistics & Probability

Frechet means and Procrustes analysis in Wasserstein space

Yoav Zemel et al.

BERNOULLI (2019)

Article Computer Science, Software Engineering

Spherical optimal transportation

Li Cui et al.

COMPUTER-AIDED DESIGN (2019)

Article Computer Science, Software Engineering

A geometric view of optimal transportation and generative model

Na Lei et al.

COMPUTER AIDED GEOMETRIC DESIGN (2019)

Article Mathematics, Interdisciplinary Applications

Statistical Aspects of Wasserstein Distances

Victor M. Panaretos et al.

ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, VOL 6 (2019)

Article Computer Science, Artificial Intelligence

Computational Optimal Transport

Gabriel Peyre et al.

FOUNDATIONS AND TRENDS IN MACHINE LEARNING (2019)

Article Computer Science, Information Systems

Optimal Transport for Gaussian Mixture Models

Yongxin Chen et al.

IEEE ACCESS (2019)

Proceedings Paper Computer Science, Artificial Intelligence

Max-Sliced Wasserstein Distance and its use for GANs

Ishan Deshpande et al.

2019 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2019) (2019)

Proceedings Paper Computer Science, Artificial Intelligence

Sliced Wasserstein Generative Models

Jiqing Wu et al.

2019 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2019) (2019)

Article Mathematics, Applied

On parameter estimation with the Wasserstein distance

Espen Bernton et al.

INFORMATION AND INFERENCE-A JOURNAL OF THE IMA (2019)

Article Statistics & Probability

Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications

Jeremie Bigot et al.

ELECTRONIC JOURNAL OF STATISTICS (2019)

Article Mathematics, Applied

Uncoupled isotonic regression via minimum Wasserstein deconvolution

Philippe Rigollet et al.

INFORMATION AND INFERENCE-A JOURNAL OF THE IMA (2019)

Article Computer Science, Artificial Intelligence

Wasserstein discriminant analysis

Remi Flamary et al.

MACHINE LEARNING (2018)

Article Computer Science, Artificial Intelligence

Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning

Morgan A. Schmitz et al.

SIAM JOURNAL ON IMAGING SCIENCES (2018)

Article Mathematics, Applied

GEODESIC PCA VERSUS LOG-PCA OF HISTOGRAMS IN THE WASSERSTEIN SPACE

Elsa Cazelles et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2018)

Article Computer Science, Software Engineering

Dynamical Optimal Transport on Discrete Surfaces

Hugo Lavenant et al.

ACM TRANSACTIONS ON GRAPHICS (2018)

Proceedings Paper Computer Science, Artificial Intelligence

Generative Modeling using the Sliced Wasserstein Distance

Ishan Deshpande et al.

2018 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR) (2018)

Article Statistics & Probability

Post-selection inference for 1-penalized likelihood models

Jonathan Taylor et al.

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE (2018)

Proceedings Paper Computer Science, Theory & Methods

Dynamical Optimal Transport on Discrete Surfaces

Hugo Lavenant et al.

SIGGRAPH ASIA'18: SIGGRAPH ASIA 2018 TECHNICAL PAPERS (2018)

Article Physics, Multidisciplinary

On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests

Aaditya Ramdas et al.

ENTROPY (2017)

Article Computer Science, Artificial Intelligence

Optimal Transport for Domain Adaptation

Nicolas Courty et al.

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (2017)

Article Computer Science, Software Engineering

Entropic Metric Alignment for Correspondence Problems

Justin Solomon et al.

ACM TRANSACTIONS ON GRAPHICS (2016)

Article Statistics & Probability

EXACT POST-SELECTION INFERENCE, WITH APPLICATION TO THE LASSO

Jason D. Lee et al.

ANNALS OF STATISTICS (2016)

Article Statistics & Probability

Exact Post-Selection Inference for Sequential Regression Procedures

Ryan J. Tibshirani et al.

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (2016)

Article Computer Science, Artificial Intelligence

Sliced and Radon Wasserstein Barycenters of Measures

Nicolas Bonneel et al.

JOURNAL OF MATHEMATICAL IMAGING AND VISION (2015)

Article Statistics & Probability

On the rate of convergence in Wasserstein distance of the empirical measure

Nicolas Fournier et al.

PROBABILITY THEORY AND RELATED FIELDS (2015)

Article Statistics & Probability

VALID POST-SELECTION INFERENCE

Richard Berk et al.

ANNALS OF STATISTICS (2013)

Article Mathematics

High-dimensional integration: The quasi-Monte Carlo way

Josef Dick et al.

ACTA NUMERICA (2013)

Article Statistics & Probability

The phylogenetic Kantorovich-Rubinstein metric for environmental sequence samples

Steven N. Evans et al.

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY (2012)

Article Computer Science, Theory & Methods

Sublinear Time Algorithms for Earth Mover's Distance

Khanh Do Ba et al.

THEORY OF COMPUTING SYSTEMS (2011)

Article Statistics & Probability

On directional regression for dimension reduction

Bing Li et al.

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (2007)

Article Computer Science, Artificial Intelligence

Automated colour grading using colour distribution transfer

Francois Pitie et al.

COMPUTER VISION AND IMAGE UNDERSTANDING (2007)