Search
Search Results
-
Right Mean for the α − z Bures-Wasserstein Quantum Divergence
The optimization problem to minimize the weighted sum of α − z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has...
-
Distributionally robust mean-absolute deviation portfolio optimization using wasserstein metric
Data uncertainty has a great impact on portfolio selection. Based on the popular mean-absolute deviation (MAD) model, we investigate how to make...
-
-
A kernel formula for regularized Wasserstein proximal operators
We study a class of regularized proximal operators in Wasserstein-2 space. We derive their solutions by kernel integration formulas. We obtain the...
-
Nonlocal Wasserstein distance: metric and asymptotic properties
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of...
-
Scalable Gromov–Wasserstein Based Comparison of Biological Time Series
A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that...
-
Coarse Embeddability of Wasserstein Space and the Space of Persistence Diagrams
We prove an equivalence between open questions about the embeddability of the space of persistence diagrams and the space of probability...
-
-
A comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton–Jacobi equations in the space of probability...
-
Strong posterior contraction rates via Wasserstein dynamics
In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small...
-
Well-posedness for Hamilton–Jacobi equations on the Wasserstein space on graphs
In this manuscript, given a metric tensor on the probability simplex, we define differential operators on the Wasserstein space of probability...
-
Viscosity Solutions of the Eikonal Equation on the Wasserstein Space
Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space....
-
Topological properties of convex order in Wasserstein metric spaces
Martingale optimal transportation has gained significant attention in mathematical finance due to its applications in pricing and hedging. A key...
-
Two-Variable Wasserstein Means of Positive Definite Operators
We investigate the two-variable Wasserstein mean of positive definite operators, as a unique positive solution of the nonlinear equation obtained...
-
On the Existence of Monge Maps for the Gromov–Wasserstein Problem
The Gromov–Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures...
-
Data-Driven Distributionally Robust Risk-Averse Two-Stage Stochastic Linear Programming over Wasserstein Ball
In this paper, we consider a data-driven distributionally robust two-stage stochastic linear optimization problem over 1-Wasserstein ball centered at...
-
A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent
... -
Exact weights, path metrics, and algebraic Wasserstein distances
We use weights on objects in an abelian category to define what we call a path metric. We introduce three special classes of weight: those compatible...
