New framework for optimal transport with jumps over intermediate spaces.
problem Optimal transport with mass jumps over intermediate spaces.
method Hierarchical Jump multi-marginal transport (HJMOT) on Polish spaces.
result Existence and uniqueness of Monge solutions under sequential differentiability and twist condition.
On compact manifolds which are not simply connected, we prove the existence of "fake" solutions to the optimal transportion problem. These maps preserve volume and arise as the exponential of a closed 1 form, hence appear geometrically like optimal transport maps. The set of such solutions forms a manifold with dimensi…
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Ampère type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this evolution equation to the stationary solution of the optimal transport problem. We …
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal tran…
Efficient federated algorithm for calculating transportation barycenter.
problem Efficiently calculating the free-support transportation barycenter in a federated setting.
method Single-loop dual decomposition algorithm that uses only aggregated information.
result Significantly scalable and low-complexity algorithm for federated computation.
The paper calibrates SPX and VIX options using optimal transport.
problem Joint calibration of SPX and VIX options or futures.
method Semimartingale optimal transport problem with PDE formulation and dual formulation.
result The model accurately calibrates SPX, VIX options, and futures simultaneously.
Noise stabilizes solutions to transport equations, preventing blow-up.
problem Proving global existence and uniqueness of solutions to stochastic transport equations.
method Characteristics-based techniques exploiting the geometric structure of transport equations.
result Noise prevents blow-up in deterministic solutions and ensures global existence and uniqueness of solutions.
Optimal Transport enhances machine learning with new methods.
problem Comparing and manipulating probability distributions in machine learning.
method Probabilistic framework rooted in rich history and theory.
result New solutions in generative modeling and transfer learning.
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.
The paper explores rectified flows and their relation to optimal transport.
problem Understanding the connection between rectified flows and optimal transport.
method Investigates invariance properties, explicit constructions, and analysis of rectified flows in various settings.
result Rectified flows, when gradient constrained, do not generally solve optimal transport problems.
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the po…
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.
Survey of linking information geometry and optimal transport.
problem Connecting two geometric frameworks for probability measures.
method Exploration of interactions and links between information geometry and optimal transport.
result Outstanding questions for both disciplines.
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…
Efficiently predicts optimal transport plans using sliced potentials.
problem Predicting optimal transport plans across multiple measure pairs efficiently.
method Regression-based and objective-based amortization strategies using sliced optimal transport potentials.
result Efficient and accurate prediction of optimal transport plans for various tasks.
Grogan et al [11,12] have recently proposed a solution to colour transfer by minimising the Euclidean distance L2 between two probability density functions capturing the colour distributions of two images (palette and target). It was shown to be very competitive to alternative solutions based on Optimal Transport for c…
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
Solves label switching in mixture models using optimal transport.
problem Label switching in mixture model posterior inference prevents meaningful statistics assessment.
method Proposes an algorithm leveraging optimal transport to compute posterior statistics in a quotient space.
result Demonstrates advantages over alternative approaches on simulated and real data.
Discontinuous Finite Element Methods (DFEM) have been widely used for solving Sn radiation transport problems in participative and non-participative media. In the DFEM Sn methodology, the transport equation is discretized into a set of algebraic equations that have to be solved for each spatial cell and angular d…
Survey revisits Bachelier and Dupire, highlighting optimal transport's role.
problem Finding arbitrage-free models calibrated to volatility surfaces.
method Revisits mathematical finance principles, uses optimal transport results.
result Optimal transport provides rigorous foundations for Dupire's model.
A new probabilistic framework for optimal transport using collective graphical models.
problem Measuring similarity between probability distributions and histograms.
method Probabilistic Optimal Transport based on Collective Graphical Models.
result OT with entropic regularization is equivalent to maximizing a posterior probability of a CGM.
We study the mean curvature flow with given non-smooth transport term and forcing term, in suitable Sobolev spaces. We prove the global existence of the weak solutions for the mean curvature flow with the terms, by using the modified Allen-Cahn equation that holds useful properties such as the monotonicity formula.
LazyDINO efficiently solves high-dimensional Bayesian inverse problems with fast and scalable solutions.
problem High-dimensional nonlinear Bayesian inverse problems with expensive parameter-to-observable maps.
method LazyDINO combines derivative-informed neural surrogates and lazy map variational inference for efficient posterior approximation.
result Significant cost reduction in amortized Bayesian inversion, achieving one to two orders of magnitude improvement.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
problem Regularity of transport map and potential on simplex boundary.
method Boundary regularity results for optimal transport maps, exploiting simplex symmetries.
result Regularity properties of transport map and its convex potential.
BalLOT uses optimal transport for balanced k-means clustering.
problem Balanced k-means clustering of data. method BalLOT is an optimal transport approach to alternating minimization.
result BalLOT provides theoretical guarantees for exact and partial recoveries of planted clusters.
New metric for probability measures connects physics and geometry.
problem Developing a new metric for probability measures.
method Transport Hessian metric, formulated dynamical systems.
result Connections to physics equations and mathematical models.
Improved Sinkhorn algorithm for UOT with near-linear complexity.
problem Solving the entropic regularized Unbalanced Optimal Transport problem efficiently.
method Geometric convergence analysis of Sinkhorn updates and primal solution properties.
result Near-linear time complexity for finding ε-approximate UOT solutions. We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
problem Matching objects between incomparable spaces using the Gromov-Wasserstein distance.
method Semi-definite programming (SDP) relaxation of the GW distance.
result The SDP relaxation provides globally optimal solutions for the GW distance in some instances.
We discuss in this note applications of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) to numerical solutions of partial differential equations arising from stochastic models in quantitative finance. In particular, we develop a framework for solving Black-Scholes-type equations by first t…
This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.
problem Finite-dimensional solutions for general Gaussian multivariate models.
method Recursive formulation of the Sinkhorn algorithm for Gaussian models, including closed form expressions of entropic transport maps and Schrödinger bridges.
result Refined convergence analysis of Gaussian Sinkhorn algorithms.
Paper proposes a new method for regression using optimal transport cost optimization.
problem Regression problem, especially with complex noise forms.
method Directly optimizes the optimal transport cost between true and estimated distributions.
result Achieves state-of-the-art results on various datasets.
New control methods improve dynamic measure transport paths.
problem Improving paths for dynamic measure transport.
method Connecting mean-field games to optimization problems for learning paths, advocating for smoothness of velocities.
result Our method recovers more efficient and smooth transport models compared to untilted paths.
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.
Meta Optimal Transport learns from past problems to solve similar OT problems faster.
problem Solving similar optimal transport problems repeatedly from scratch is inefficient.
method Amortized optimization to predict optimal transport maps from past solutions.
result Meta OT models can solve new problems faster than standard methods.
This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.
problem Approximating the Laplace-Beltrami operator using optimal transport with quadratic regularization.
method Deriving first-order optimal potentials and analyzing the convergence of discrete Laplace operators.
result The discrete Laplace operators converge to the Laplace-Beltrami operator on smooth manifolds.
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.
Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the cost is given by minimizing a Lagrangian action.
Unified framework for ensemble transport-based smoothing of non-Gaussian time series.
problem Bayesian time series re-analysis with non-Gaussian distributions.
method Measure transport approach to derive consistent prior-to-posterior transformations.
result General ensemble framework for transport-based smoothing of state-space models.
Dynamic reinsurance aims to minimize surplus risk using martingale transport.
problem Minimizing surplus risk in dynamic reinsurance.
method Martingale optimal transport techniques.
result A tractable solution analogous to the Bass martingale is found.
Survey of Sinkhorn algorithm for optimal transport, emphasizing its geometric origins.
problem Solving optimal transport problems efficiently and accurately.
method Discretization of a non-linear integral equation.
result Geometric interpretation and discretization of the Sinkhorn algorithm.
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 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.
New method calculates cut locus on Riemannian manifolds using optimal transport.
problem Computing the cut locus on compact Riemannian manifolds.
method Characterization via optimal transport density solution of Monge-Kantorovich equations, numerical approximation.
result Proposed novel framework for numerical approximation of cut locus.
Optimal transport is #P-hard when components are independent, even with approximate solutions.
problem Computational complexity of optimal transport with independent marginals.
method Proved #P-hardness and developed a pseudo-polynomial time approximation algorithm.
result Optimal transport is #P-hard even with independent components and approximate solutions.
New framework enhances neural network robustness against adversarial attacks.
problem Vulnerability of deep neural networks to small perturbations.
method Integrates Lipschitz constraint using optimal transport and hinge regularization.
result Proposes a new loss function that certifies adversarial robustness.
s-OTDD compares datasets efficiently without training, robust to class variations.
problem Efficiently compare datasets without training or class variations.
method Moment Transform Projection (MTP) and sliced optimal transport.
result s-OTDD correlates with optimal transport and transfer learning performance.
Accelerates optimal transport computation by 10x with spectral insights.
problem Exponential slow-down of convergence in Entropic Optimal Transport as regularization weakens.
method Spectral insights and spectral warm-start strategy to mitigate convergence issues.
result Faster convergence compared to the reference method Sinkhorn algorithm.