30 citations · 180 across the 40 of their papers we have counts for
6 papers · 1 filter
Wasserstein-Cramér-Rao Theory of Unbiased Estimation
Nicolás García Trillos, Adam Quinn Jaffe, Bodhisattva Sen
The quantity of interest in the classical Cramér-Rao theory of unbiased estimation (e.g., the Cramér-Rao lower bound, its exact attainment for exponential families, and asymptotic…
Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions
Camilo Andrés García Trillos, Nicolás García Trillos
We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-a…
The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)
Andrew Ferguson, Marisa LaFleur, Lars Ruthotto +97
This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 w…
Central limit theorems for the eigenvalues of graph Laplacians on data clouds
Chenghui Li, Nicolás García Trillos, Housen Li +1
Given i.i.d.\ samples from a distribution supported on a low dimensional manifold embedded in Eucliden space, we consider the graph Laplacian ope…
Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
Nicolás García Trillos, Chenghui Li, Raghavendra Venkatraman
We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution supported on a manifold . The operators discussed in the pape…
Vector valued optimal transport: from dynamic to static formulations
Katy Craig, Nicolás García Trillos, Đorđe Nikolić
Motivated by applications in classification of vector valued measures and multispecies PDE, we develop a theory that unifies existing notions of vector valued optimal transport, fr…