Stability proved for martingale and weak transport problems.
problem Stability of martingale and weak optimal transport problems.
method Established stability through unconventional topology considering temporal structure of martingales.
result Proved stability of martingale and weak transport problems.
Deep learning models optimize urban transportation scheduling.
problem Optimizing transportation systems with complex dynamics and large data sets.
method Developed deep learning metamodels for simulators and reinforcement learning algorithms.
result Improved optimal scheduling of travelers on transportation networks.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.
Solves optimal transport in Lorentz-Finsler spacetimes, generalizing previous work.
problem Optimal transport in Lorentz-Finsler geometry.
method Solves the Kantorovich and Monge problems for globally hyperbolic Lorentz-Finsler spacetimes.
result Generalizes previous results on optimal transport in spacetimes.
Extends optimal transport to dynamic and martingale settings.
problem Dynamic and martingale relaxation of optimal transport problems.
method Extends Benamou-Brenier formula to weak optimal transport and introduces barycentric optimal transport.
result Relates barycentric optimal transport to martingale Benamou-Brenier formula.
Paper uses neural networks to solve complex transport problems.
problem Optimal transport and related hedging problems.
method Penalization and neural networks to solve optimization problems.
result Effective solution to multi-marginal, martingale optimal transport problems.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
A new framework SPOT efficiently solves large scale optimal transport problems.
problem Heavy computational burden in optimal transport limits its use.
method Implicit generative learning framework (SPOT) approximates optimal transport plan and solves it using stochastic gradient algorithms.
result SPOT efficiently solves optimal transport problems and can recover the density of the plan.
A novel Federated Learning scheme using Optimal Transport for personalized model training.
problem Training models with data from clients having non-identically distributed data.
method Personalized Federated Learning scheme based on Optimal Transport (FedOT).
result FedOT scheme effectively transfers data from multiple distributions to a common domain and optimizes the prediction model.
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.
The paper solves optimal transport problems with domain constraints.
problem Optimal transport problems with domain constraints.
method Characterizes existence of a probability measure with convex transport constraints.
result Obtains Kantorovich duality and monotonicity principle.
Study investigates duality and dual optimizers for various transport problems.
problem Existence and characterization of dual optimizers for adapted transport problems.
method Minimal assumptions, including causal and bicausal settings, are considered.
result No-arbitrage assumption leads to multicausal couplings and equivalent robust superhedging price computation.
New algorithm improves on existing methods for solving transport problems.
problem Finding a map to transport one distribution to another.
method Iterative Markovian Fitting (IMF) and Diffusion Schrödinger Bridge Matching (DSBM).
result DSBM significantly improves over previous SB numerics and recovers various transport methods.
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the hi…
Unified deep learning framework solves various optimal transport problems.
problem Solving variational problems in optimal transport with computational challenges.
method Unified deep learning framework leveraging dual formulation of Lagrangians.
result Outperforms previous approaches in single-cell trajectory inference.
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.
Proves hardness of semi-discrete optimal transport and proposes regularization methods.
problem Computing Wasserstein distance between discrete and non-discrete probability measures.
method Proves hardness, introduces distributionally robust dual optimal transport, regularizes primal objective, uses stochastic gradient descent.
result Regularization schemes and improved convergence guarantees for semi-discrete optimal transport problems.
Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.
problem Adapting optimal transport for ε-contaminated sets. method Generalized optimal transport problems with lower probabilities, showing equivalence under ε-contaminations. result Monge's and Kantorovich's problems coincide under ε-contaminated sets, but not always. 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.
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All metrics (resp. transports) consistent with a given transport (resp. metric) are e…
A new clustering method using transportation distance for multilevel data.
problem Multilevel clustering problems, especially with large datasets.
method Probabilistic approach based on composite transportation distance, solving a joint optimization problem over probability measures.
result Efficient and scalable solution for multilevel datasets, demonstrated on synthetic and real data.
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.
New computational methods solve martingale optimal transport problems.
problem Solving martingale optimal transport problems with additional dynamics constraints.
method Discretization of marginal distributions combined with linear programming and entropic regularisation.
result Approximation of the MOT value using linear programming problems.
A new method for efficient optimal partial transport in 1D.
problem Limitation of equal mass assumption in optimal transport.
method Sliced Optimal Partial Transport (Sliced-OPT) algorithm.
result Sliced-OPT demonstrates computational and accuracy benefits.
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
New algorithm detects anomalies by forcing samples to displace mass in low-density regions.
problem Detecting anomalies in datasets.
method Mass Repulsing Optimal Transport (MROT) approach.
result Our algorithm improves anomaly detection over existing methods.
A mesh-free method solves continuum-marginal optimal transport problems.
problem Recovering minimum-energy velocity fields from time-continuous probability marginals.
method Embeds weak continuity equation in a reproducing kernel Hilbert space, optimizing with mini-batch stochastic methods.
result Accurately recovers drift and maintains marginal consistency in synthetic experiments.
Exponential rate of convergence for optimal mass transport solutions.
problem Optimal mass transport on bounded domains.
method Differential Harnack inequality and techniques specific to mass transport.
result Exponential convergence of solutions to the parabolic equation to the stationary solution.
Study uses machine learning to recommend best solvers for slab transport problems.
problem Auto-selecting the best solvers for transport problems in uniform slabs.
method Three solvers (Richardson, diffusion synthetic acceleration, nonlinear diffusion acceleration) and five machine learning algorithms (linear discriminant analysis, K-nearest neighbors, support vector machine, random forest, neural networks) were tested.
result Random forest and K-nearest neighbors showed potential as best solvers for classification problems.
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.
Wasserstein GANs with Gradient Penalty compute a different optimal transport problem called congested transport.
problem Training generative models to produce high-quality synthetic data.
method Wasserstein GANs with Gradient Penalty (WGAN-GP) approach to calculate the Wasserstein 1 distance.
result WGAN-GP computes the minimum of the congested transport problem, not the Wasserstein 1 distance.
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.
Develops theory for conditional optimal transport in infinite-dimensional spaces.
problem Bayesian inference with functional parameters in infinite-dimensional spaces.
method Theory of constrained optimal transport for block-triangular maps.
result Regularity estimates on conditioning maps from prior to posterior.
Optimal transport with scalar martingales defined over multiple periods.
problem Finding optimal transport plans with specific properties over multiple time periods.
method Introducing left-monotone transports and characterizing them through various properties.
result Left-monotone transports are unique under certain conditions and have specific order properties.
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.
Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.
problem Entropy Martingale Optimal Transport problem and its associated optimization problem.
method Combines Entropy Optimal Transport and Martingale Optimal Transport theories, with novel penalization terms and constraints.
result Establishes a nonlinear robust pricing-hedging duality, covering various known robust results.
A new algorithm speeds up optimal transport for machine learning.
problem Optimal transport for machine learning with additional terms.
method Forward-backward splitting algorithm based on Bregman distances.
result Significant improvement in speed and performance for domain adaptation.
New toolkit for directed distances improves flexibility of OT problems.
problem Optimal transport problems with constraints.
method Directed distances between quantile functions.
result Flexibility in solving OT problems enhanced.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
problem Bayesian filtering for nonlinear systems with non-Gaussian observations.
method Optimal transport theory applied to Bayes' law, constructing Brenier maps.
result New variational formulations of EnKF and FPF for non-Gaussian settings.
Paper compares neural network approaches to Optimal Transport.
problem Learning Optimal Maps between probability distributions.
method Two categories of approaches: heuristic and math-justified. Novel approach involves dynamic flows and supervised learning.
result Novel approach involving dynamic flows and reductions of Optimal Transport to supervised learning.
Study MinMax methods for optimization problems, including optimal transport.
problem Optimization problems, especially optimal transport.
method MinMax framework, regularization, neural networks, approximation theorems.
result Justification of neural networks for solving optimization problems.
A JAX toolbox solves optimal transport problems for point clouds and histograms.
problem Optimal transport problems between point clouds and histograms.
method Automatic and custom reverse mode differentiation, vectorization, just-in-time compilation, and accelerators support.
result Solves a wide range of optimal transport problems including regularized OT, barycenters, Gromov-Wasserstein, and low-rank solvers.
Research shows no dual solutions for Lorentzian cost functions in general, but proves their existence under certain conditions.
problem Existence of dual solutions for Lorentzian cost functions in optimal transportation problems.
method Analyzes dual problem in Lorentz-Finsler geometry, proves existence under natural assumptions, and shows implications for optimal transport.
result Existence of dual solutions under specific conditions, implying timelike optimal transport on a set of full measure.
Estimates discontinuous optimal transport maps between a discrete and continuous distribution.
problem Estimating discontinuous optimal transport maps between a discrete and continuous distribution.
method Entropic optimal transport estimator, computationally efficient.
result The estimator converges at the minimax-optimal rate n−1/2 in the semi-discrete setting. Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.
problem Optimal transport between SPD matrix-valued measures.
method Formulated as a generalized optimal transport problem with block SPD matrices, endowed with a novel Riemannian manifold structure.
result The novel Riemannian manifold allows solving SPD matrix-valued optimal transport problems using Riemannian optimization.
New forms of multi-marginal POT problem derived for computational efficiency.
problem Optimizing transport between multiple unbalanced measures with limited supports.
method Developed two equivalence forms of the POT problem and an optimization algorithm, ApproxMPOT.
result ApproxMPOT algorithm achieves optimal value with complexity ildeO(m3(n+1)m/ε2). Abstract theory extends optimal transport to Banach lattices.
problem Generalize optimal transport theory to Banach lattices.
method Abstract framework, duality theory, Banach lattice, order unit.
result Characterization of dual elements for generalized optimal transport.
Optimal transport framework for zero-shot learning.
problem Generalized zero-shot learning of unseen classes.
method Conditional generative model and optimal transport between generated and real features.
result Optimal transport-based method outperforms state-of-the-art methods.