Nicolás García Trillos

Matt Jacobs

Jakwang Kim

Matthew Werenski

CoRR, 2024

2023

The multimarginal optimal transport formulation of adversarial multiclass classification.

[BibT_eX]

[DOI]

Matt Jacobs

Jakwang Kim

J. Mach. Learn. Res., 2023

Large sample spectral analysis of graph-based multi-manifold clustering.

[BibT_eX]

[DOI]

Pengfei He

Chenghui Li

J. Mach. Learn. Res., 2023

A New Perspective On Denoising Based On Optimal Transport.

[BibT_eX]

[DOI]

Bodhisattva Sen

CoRR, 2023

Spectral Neural Networks: Approximation Theory and Optimization Landscape.

[BibT_eX]

[DOI]

Chenghui Li

Rishi Sonthalia

CoRR, 2023

Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms.

[BibT_eX]

[DOI]

Anna Little

Daniel McKenzie

James M. Murphy

CoRR, 2023

Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds.

[BibT_eX]

[DOI]

Melanie Weber

CoRR, 2023

It begins with a boundary: A geometric view on probabilistically robust learning.

[BibT_eX]

[DOI]

Leon Bungert

CoRR, 2023

FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization.

[BibT_eX]

[DOI]

Jose A. Carrillo

Sixu Li

Yuhua Zhu

CoRR, 2023

On the existence of solutions to adversarial training in multiclass classification.

[BibT_eX]

[DOI]

Matt Jacobs

Jakwang Kim

CoRR, 2023

On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it.

[BibT_eX]

[DOI]

Camilo Garcia Trillos

CoRR, 2023

2022

Lipschitz Regularity of Graph Laplacians on Random Data Clouds.

[BibT_eX]

[DOI]

Jeff Calder

Marta Lewicka

SIAM J. Math. Anal., 2022

Semi-discrete Optimization Through Semi-discrete Optimal Transport: A Framework for Neural Architecture Search.

[BibT_eX]

[DOI]

Javier Morales

J. Nonlinear Sci., 2022

Adversarial Classification: Necessary Conditions and Geometric Flows.

[BibT_eX]

[DOI]

J. Mach. Learn. Res., 2022

Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks.

[BibT_eX]

[DOI]

Aditya Kumar Akash

Sixu Li

CoRR, 2022

Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective.

[BibT_eX]

[DOI]

Yuetian Luo

CoRR, 2022

Rates of Convergence for Regression with the Graph Poly-Laplacian.

[BibT_eX]

[DOI]

Matthew Thorpe

CoRR, 2022

Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning.

[BibT_eX]

[DOI]

Ruiyi Yang

CoRR, 2022

2021

Geometric structure of graph Laplacian embeddings.

[BibT_eX]

[DOI]

Franca Hoffmann

Bamdad Hosseini

J. Mach. Learn. Res., 2021

The Geometry of Adversarial Training in Binary Classification.

[BibT_eX]

[DOI]

Leon Bungert

CoRR, 2021

On the regularized risk of distributionally robust learning over deep neural networks.

[BibT_eX]

[DOI]

Camilo Garcia Trillos

CoRR, 2021

Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation.

[BibT_eX]

[DOI]

Katy Craig

Dejan Slepcev

CoRR, 2021

Traditional and Accelerated Gradient Descent for Neural Architecture Search.

[BibT_eX]

[DOI]

Félix Morales

Javier Morales

Proceedings of the Geometric Science of Information - 5th International Conference, 2021

2020

A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors.

[BibT_eX]

[DOI]

Ryan W. Murray

SIAM J. Math. Data Sci., 2020

On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms.

[BibT_eX]

[DOI]

Zachary Kaplan

Thabo Samakhoana

J. Mach. Learn. Res., 2020

Error Estimates for Spectral Convergence of the Graph Laplacian on Random Geometric Graphs Toward the Laplace-Beltrami Operator.

[BibT_eX]

[DOI]

Moritz Gerlach

Matthias Hein

Dejan Slepcev

Found. Comput. Math., 2020

From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds.

[BibT_eX]

[DOI]

Matthew Thorpe

CoRR, 2020

Data-Driven Forward Discretizations for Bayesian Inversion.

[BibT_eX]

[DOI]

Daniele Bigoni

Yuming Chen

Youssef M. Marzouk

CoRR, 2020

2019

Variational Limits of k-NN Graph-Based Functionals on Data Clouds.

[BibT_eX]

[DOI]

SIAM J. Math. Data Sci., 2019

Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis.

[BibT_eX]

[DOI]

Ruiyi Yang

J. Mach. Learn. Res., 2019

Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning.

[BibT_eX]

[DOI]

Zachary Kaplan

Entropy, 2019

Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs.

[BibT_eX]

[DOI]

Jeff Calder

CoRR, 2019

2018

Continuum Limits of Posteriors in Graph Bayesian Inverse Problems.

[BibT_eX]

[DOI]

SIAM J. Math. Anal., 2018

2017

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

[BibT_eX]

[DOI]

Aaditya Ramdas

Marco Cuturi

Entropy, 2017

On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms.

[BibT_eX]

[DOI]

Zachary Kaplan

Thabo Samakhoana

CoRR, 2017

2016

Consistency of Cheeger and Ratio Graph Cuts.

[BibT_eX]

[DOI]

J. Mach. Learn. Res., 2016

2015

A variational approach to the consistency of spectral clustering.

[BibT_eX]

[DOI]