NOT learns optimal transport plans, kernel costs improve performance.
problem NOT algorithm learns non-optimal plans with weak quadratic costs.
method Introduced kernel weak quadratic costs to improve NOT's performance.
result Kernel costs provide improved theoretical and practical guarantees.
Bayesian approach to optimal transport with stochastic costs.
problem Inferring optimal transport plans with uncertain costs.
method Bayesian framework and Hamiltonian Monte Carlo (HMC) sampling.
result Inference of optimal transport plans under stochastic cost functions.
New research extends optimal transport map breakdown properties to general costs.
problem Understanding robustness of optimal transport maps under contamination.
method Analyzing breakdown point of optimal transport maps for general convex costs.
result Breakdown point of optimal transport maps is independent of the cost function.
A new method for optimal transport using neural ODEs that preserves marginal constraints.
problem Optimal transport between two continuous distributions with specific cost functions.
method Iterative construction of neural ODEs to minimize transport cost while preserving marginal constraints.
result Monotonic interior approach that decreases transport cost efficiently.
Study uses weak transport for non-convex costs in fixed-income markets.
problem Characterizing optimal caplet pricing in fixed-income markets.
method Introduced weak optimal transport for non-convex costs, reduced general costs to convex problems.
result Established robust super-replication results for fixed-income markets.
Study optimal transport for robust optimization, showing how adversary's strategy relates to regularization.
problem Optimizing under uncertain parameters with a fictitious adversary reshaping a reference distribution.
method Introduces optimal transport and regularization to relate robustification to variation and Lipschitz norms.
result Conditions for existence and computability of Nash equilibrium between decision-maker and adversary.
Estimates optimal transport maps with known cost functions.
problem Ensuring optimal transport maps correspond to real-world usefulness.
method Differentiable neural ground costs with known Monge map forms.
result General approach for incorporating prior information.
Developed a cost and revenue model for HEMS to estimate breakeven transport volumes under different reimbursement and labor cost assumptions.
problem Estimating breakeven transport volumes for HEMS under varying reimbursement and labor cost assumptions.
method Developed a two-part model: cost framework and actuarial revenue model using healthcare encounter data and payer reimbursement rates.
result Estimated breakeven transport volumes under different reimbursement and labor cost assumptions.
Researchers analyze inverse optimal transport, deriving theoretical and empirical insights.
problem Understanding the inverse problem of inferring cost matrices from optimal couplings.
method Formalized and analyzed using entropy-regularized optimal transport, with theoretical and empirical contributions.
result Characterization of the manifold of cross-ratio equivalent costs and derivation of an MCMC sampler.
CR-UOT improves matching of heterogeneous single-cell omics profiles.
problem Matching nonnegative finite Radon measures across heterogeneous spaces.
method Cost-regularized unbalanced optimal transport (CR-UOT) framework.
result CR-UOT improves alignment of heterogeneous single-cell omics profiles.
SOS programming verifies MTW tensor non-negativity for optimal transport maps.
problem Verifying MTW tensor non-negativity for general cost functions is difficult.
method Sum-of-Squares (SOS) programming for verifying and approximating MTW non-negativity.
result SOS programming provides certificates and approximations of MTW non-negativity.
Researchers develop neural optimal transport with Lagrangian costs for efficient computation.
problem Optimal transport between measures with Lagrangian costs for systems with geometric constraints.
method Neural network approach to compute geodesics and optimal transport maps efficiently.
result Efficient computation of geodesics and optimal transport maps without ODE solvers.
We study a parabolic equation for finding solutions to the optimal transport problem on compact Riemannian manifolds with general cost functions. We show that if the cost satisfies the strong MTW condition and the stay-away singularity property, then the solution to the parabolic flow with any appropriate initial condi…
Paper introduces information-constrained optimal transport, generalizing Talagrand's inequality.
problem Optimal transport problem with information constraints.
method Information constrained variation of optimal transport, using Marton's approach.
result Recovery of concentration of measure results and solution to Cover's open problem.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
problem Stochastic guidance of spin states of rigid bodies over a hard deadline.
method Structural analysis of Kantorovich optimal coupling formulation for nonlinear dynamics.
result Derives the ground cost for optimal transport of angular velocity.
Derives inequality for optimal transport on manifolds.
problem Optimal transport theory on manifolds.
method Five gradients inequality for cost functions on Lie groups and Riemannian manifolds.
result Derives inequality for optimal transport on specific manifolds.
Study proves convergence of subgradients for optimal transport-based objectives.
problem Ensuring statistical consistency and optimization stability in transport-based models.
method Proves graphical convergence of subdifferentials to the subdifferential of the population objective.
result Standard subgradient methods consistently approach stationary points of the population-level problem.
New curvature measure for optimal transport with specific cost function.
problem Optimal transport with specific cost function.
method Proposed generalized curvature measure.
result Non-negativity of the generalized curvature implies displacement convexity.
A new method matches measures across different spaces using cost-regularized optimal transport.
problem Matching measures in different spaces without aligned data.
method Cost-regularized optimal transport formulation to match measures across two Euclidean spaces.
result Demonstrated applicability to single-cell spatial transcriptomics/multiomics matching tasks.
Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the mo…
Study on regularity of optimal transport maps on convex domains with quadratic cost.
problem Regularity of optimal transport maps between convex domains with quadratic cost.
method Analysis of Cα-densities and C1,α boundary conditions, monotonicity formula for optimal transport maps. result Proves C1,1−ε-regularity for nondegenerate Cα-densities and C2,α-regularity for C1,α boundary. Study optimal transport on globally hyperbolic spacetimes, focusing on weak Kantorovich potentials' regularity.
problem Investigate regularity of weak Kantorovich potentials on globally hyperbolic spacetimes.
method Apply insights from Riemannian and Lorentzian cases to study π-solutions. result Conclude existence, uniqueness, and structure of optimal transport maps.
Extends Optimal Transport to multiple agents, aiming for equitable and optimal distribution.
problem Sharing costs or goods equitably among multiple agents with different preferences.
method Minimizes the maximum transportation cost or maximizes the minimum utility.
result Provides a new algorithm faster than standard linear programming.
We give sufficient conditions on initial and target measures supported on the sphere §n to ensure the solution to the optimal transport problem with the cost ∣x−y∣2/2 is a diffeomorphism.
A framework for cost of belief revision in uncertain agents.
problem Cost of revising beliefs in uncertain agents.
method Axiomatic framework for transport-based belief costs, postulates P0 and P1.
result Cost metric is conformally reweighted by Fisher information, leading to a cost floor diverging at certainty.
Paper introduces a neural network for consistent estimation of optimal transport maps.
problem Statistically consistent estimation of optimal transport maps between probability distributions.
method Lipschitz-constrained GAN penalized by quadratic transportation cost.
result The generator converges uniformly to the optimal transport map as sample size increases.
We investigate the use of entropy-regularized optimal transport (EOT) cost in developing generative models to learn implicit distributions. Two generative models are proposed. One uses EOT cost directly in an one-shot optimization problem and the other uses EOT cost iteratively in an adversarial game. The proposed gene…
Study timelike Ricci curvature bounds via optimal transport with Orlicz-type costs.
problem Characterize timelike Ricci curvature bounds.
method Optimal transport with Orlicz-type costs, convexity of relative entropy.
result Characterize timelike Ricci curvature lower bounds via convexity of relative entropy.
New proof of energy functional monotonicity via geodesics in measure space.
problem Proving monotonicity of energy functional in generalized Ricci flow.
method Defining adapted cost functional, geodesics, and entropy functional.
result Monotonicity of cost along backwards heat flow and energy functional along generalized Ricci flow.
New algorithms solve weak optimal transport problems for nonlinear costs.
problem Computing weak optimal transport with nonlinear costs.
method Mirror descent algorithms for primal and dual versions of WOT.
result Solutions for WOT and WOTUK compared with classical OT.
Study optimal transport for stationary processes, estimating joinings and costs.
problem Optimal transport for stationary stochastic processes.
method Introduced estimators for optimal joinings and costs, established consistency and error rates.
result Consistent estimators of optimal joinings and costs under mild and stronger mixing assumptions.
New interpretation of OT regularization as adversarial ground cost.
problem Optimal transport (OT) regularization for machine learning.
method Using Fenchel duality, interpret convex OT regularization as adversarial ground cost.
result Access to a robust dissimilarity measure on the ground space.
A new method detects and corrects outliers using optimal transport.
problem Outliers in data can skew estimation results, leading to inaccurate conclusions.
method Optimal transport with a concave cost function for outlier detection and correction.
result The method effectively identifies and corrects outliers, improving estimation accuracy.
Optimal transport theory applied to quantum states on Grassmannians.
problem Developing optimal transport for quantum states.
method Metric geometry of Grassmannians and spectral theorem for density matrices.
result Wasserstein distance for normal states of von Neumann algebras.
New geometry for optimal transport cost based on Bregman divergences.
problem Optimal transport cost calculation with Bregman divergences.
method Established properties, defined interpolations, constructed dualistic geometry.
result Derived generalized Pythagorean inequality and Bregman-Wasserstein barycenters.
Paper solves inverse optimal transport problem with convex optimization and neural network.
problem Learning the cost function for optimal transport from observed data.
method Unconstrained convex optimization, Sinkhorn-Knopp algorithm, and deep neural network parameterization.
result Novel framework avoids repeated OT solving, demonstrating efficiency and accuracy.
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
problem Numerical instabilities in training Wasserstein Generative Adversarial Networks (WGAN).
method Valid differentiation theorem for entropic regularized transport, semi-discrete gradient formulation, and optimization algorithm.
result Existence of optimal transport gradient for generative models under specified conditions.
Study non-Gaussian measures' concentration properties in metric spaces.
problem Concentration properties for non-linear Gaussian functionals with non-Gaussian tails.
method Prove generalised Transportation-Cost Inequalities (TCIs) for specific functionals.
result Extended TCIs for rough volatility and Parabolic Anderson Model.
In this paper the regularity of optimal transportation potentials defined on round spheres is investigated. Specifically, this research generalises the calculations done by Loeper, where he showed that the strong (A3) condition of Trudinger and Wang is satisfied on the round sphere, when the cost-function is the geodes…
In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type dr,r>1, where d is the Riemannian distance of a complete …
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs, where the Euclidean distance is implicitly used, this new method allows …
Study optimal transport costs with zero MTW tensor, finding new families of costs and divergence functions.
problem Characterize optimal transport costs with zero MTW tensor.
method Optimal transport theory, information geometry, solving nonlinear ODEs.
result Found new families of costs and divergence functions.
The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of the transport paths is studied. These results generalize parts of Bertrand & Puel…
Given a transportation cost c:M×Mˉ→R, optimal maps minimize the total cost of moving masses from M to Mˉ. We find a pseudo-metric and a calibration form on M×Mˉ such that the graph of an optimal map is a calibrated maximal submanifold. We define the mass of space-like current…
New geometric approach gives apriori estimate for optimal transport maps.
problem Proving regularity of optimal transport maps under Ma--Trudinger--Wang condition.
method Geometric derivation using pseudo-Riemannian geometry.
result New derivation of C1 interior estimate for optimal maps. This paper explores how entropic regularization improves Wasserstein estimators' performance.
problem Improving the approximation and estimation properties of Wasserstein estimators.
method Entropic regularization of optimal transport costs to smooth Wasserstein estimators.
result Entropic regularization can achieve comparable statistical performance to un-regularized estimators at lower computational cost.
In this paper, it is shown that the reduced ℓp-cohomology is trivial for a class of finitely generated amenable groups called transport amenable. These groups are those for which there exist a sequence of measures ξn converging to a left-invariant mean and such that the transport cost between ξn displaced b…
This article presents results from the first statistically significant study of cost escalation in transportation infrastructure projects. Based on a sample of 258 transportation infrastructure projects worth US$90 billion and representing different project types, geographical regions, and historical periods, it is fou…