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.
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.
A new method for averaging probability distributions based on optimal weak mass transport.
problem Averaging probability distributions in a geometric way.
method Weak barycenters based on optimal weak mass transport.
result Extracts common geometric information shared by all input distributions.
The paper introduces a new method for risk measurement using weak optimal transport.
problem Risk measurement in insurance and financial contexts.
method Convex risk measures with weak optimal transport penalties, explicit representation via nonlinear transform, computational aspects, and approximations using neural networks.
result Explicit representation and computational methods for risk measures.
We extend martingale transport results to weak martingale transport.
problem Applying martingale transport results to weak martingale transport.
method Change of numeraire for weak martingale transport.
result Established the correspondence between stretched Brownian motion and its geometric counterpart.
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.
Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans π1,π2,… converges weakly to a transport plan π, then π is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…
Proves stability in Weyl polytopes using optimal transport.
problem Stability of Weyl polytopes under optimal transport.
method Optimal transport stability for reflexive Weyl polytopes.
result Weak metric SYZ conjecture holds for Delzant reflexive Weyl polytopes.
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.
New emulator bridges simulators using conditional optimal transport.
problem Bridging simulators with minimal distortion.
method Flow-based approach to learn likelihood transport, COT-FM for optimal matching.
result Emulator accurately captures full correction between simulators.
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.
The study establishes stability in WMOT, crucial for finance with imprecise data.
problem Stability in weak martingale optimal transport for finance with imprecise data.
method Established stability through rigorous mathematical analysis.
result Stability of WMOT is proven, with applications to VIX futures and Brownian motion.
The paper establishes general results in Lorentzian optimal transport theory.
problem Establishing strong duality and optimality conditions in Lorentzian optimal transport.
method Providing non-trivial assumptions on measures, characterizing optimality, and proving regularity results.
result Regularity results for c-convex functions and (weak) Kantorovich potentials do not extend to the Lorentzian setting, but under suitable assumptions, they are locally semconvex. DPOT uses deep learning to compute optimal transport efficiently.
problem Computing optimal transport between continuous distributions from unpaired samples.
method DeepParticle methods for min-min optimization without network structure restrictions.
result Established weak convergence and error bounds between learned and optimal maps.
Study on stability of optimal transport problems for probability measures.
problem Stability of supermartingale optimal transport problems.
method Approximation in adapted Wasserstein distance and continuity of functional.
result Continuity and monotonicity principles for weak supermartingale optimal transport.
Extends martingale transport for robust finance problems.
problem Addressing specific robust finance problems not covered by standard martingale transport.
method Introduces an additional parameter to the weak martingale optimal transport problem and proves stability.
result Stability of the extended problem with respect to risk-neutral marginal distributions.
In this paper we apply techniques from optimal transport to study the neckpinch examples of Angenent-Knopf which arise through the Ricci flow on Sn+1. In particular, we recover their proof of 'single-point pinching' along the flow. Using the methods of optimal transportation, we are able to remove the ass…
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.
Study compares synthetic and distributional Ricci curvature bounds.
problem Comparing synthetic and distributional approaches to lower Ricci curvature bounds.
method Analyzes synthetic via weak displacement convexity and distributional via non-negativity of Ricci-tensor.
result Distributional bounds imply entropy bounds for C1 metrics and vice versa for C1,1 under convergence condition. A new algorithm for estimating continuous entropic barycenters under arbitrary costs.
problem Estimating the average of probability distributions under arbitrary cost functions.
method Dual reformulation of Entropic Optimal Transport (EOT) problem based on weak OT.
result Established quality bounds for the recovered solution and seamless integration with EBM learning.
A new method for fast optimal transport using sliced Wasserstein generalized geodesics.
problem Computing optimal transport distances efficiently and accurately.
method Proposes a new proxy of squared Wasserstein distance based on one-dimensional projections.
result min-SWGG is an upper bound of Wasserstein distance with similar computational complexity.
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.
Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.
problem Optimal transport of multiple probability distributions.
method Unified Kantorovich duality theory for multimarginal optimal transport on general Polish product spaces.
result Unified duality theory for multimarginal optimal transport, extending classical two-marginal conjugacy.
Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.
problem Synthetic curvature bounds for Lorentzian spaces.
method Optimal transport, convexity analysis of entropy functionals.
result Synthetic notion of timelike Ricci curvature lower bounds.
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
problem Tackles the martingale Schrödinger bridge in arbitrary dimensions.
method Identifies continuous-time counterpart and relates to variational problems.
result Continuous martingale Schrödinger bridge coincides with Föllmer martingale in irreducible case.
A new method selects a representative subsample for efficient kernel density estimation.
problem Selecting a representative subsample without model assumptions.
method Optimal transport techniques for model-free subsampling with an efficient algorithm.
result The selected subsample can be used for efficient density estimation with derived convergence rates and optimal bandwidth.
Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…
A general duality proof for Wasserstein distributionally robust optimization.
problem Optimizing under uncertainty with Wasserstein distance.
method One-dimensional convex analysis and interchangeability principle.
result General duality result holds for various distributions and costs.
It is shown that curvature-dimension bounds CD(N, k) for a metric measure space (X,d,m) in the sense of Sturm imply a weak L^1- Poincare-inequality under some symmetry assumption on the choice of transport rays in the cut locus of (X,d). This condition is satisfied if (X,d) has m-almost surely no branching points.
Paper introduces MSA for weakly supervised covariance alignment in MEG signals.
problem Limited labeled signals in target datasets for MEG applications.
method Mixing model Stiefel Adaptation (MSA) leveraging unlabeled data.
result MSA outperforms recent methods in brain-age regression with MEG signals.
Parallel transport defined for 2-bundles over Lie groupoids.
problem Defining parallel transport for 2-bundles over Lie groupoids.
method Using Lie 2-group torsors and pseudofunctors, extending principal 2-bundles to differentiable stacks.
result A smooth parallel transport functor defined for Haefliger paths.
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
Introduces statistical optimal transport for probabilistic lectures.
problem No specific problem stated; focuses on introduction.
method Lecture-based introduction to statistical optimal transport.
result Provides an introduction to statistical optimal transport.
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).
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.
We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded above and below. This new condition is equivalent to the weak Ma-Trudinger-Wang condition when the cost is C4. Moreover, we only require (n…
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…
New optimal transport method handles mass creation and destruction.
problem Optimal re-balancing of portfolios with mass creation or destruction.
method Formalizes an optimal transport problem with mass-change factor.
result Existence of optimal transport plans and maps established.
Review of modern computational optimal transport methods for biomedical applications.
problem Efficient computation of optimal transport for big data.
method Regularization-based and projection-based computational methods.
result Advancements in computational optimal transport methods for biomedical research.
Paper investigates optimal transport map estimation in infinite-dimensional spaces.
problem Estimating optimal transport maps in infinite-dimensional spaces is challenging.
method Characterizes γ-smoothness for optimal transport maps and develops a polynomial-rate estimator. result Shows polynomial-order minimax risk for optimal transport map estimation.
Study shows how optimal transport behaves in higher dimensions.
problem Characterizing optimal transport in higher dimensions with Euclidean distance.
method Investigates the small regularization limit of entropic optimal transport.
result The limiting transport plan is supported on transport rays and uniquely minimizes a relative entropy functional.
A new model corrects inhomogeneity in Optimal Transport with Boundary.
problem Inhomogeneity in UROT models for Optimal Transport with Boundary.
method Proposed a modified entropic regularization term to make UROT models homogeneous.
result Homogeneous UROT model preserves properties of standard UROT while correcting inhomogeneity.
Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix factorization (NMF) algorithm for supervised speech blind source separation (BSS). Optimal …
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.
Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
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.
Alternative proof of Michael-Simon-Sobolev inequality using optimal transport.
problem Proving the Michael-Simon-Sobolev inequality for submanifolds of codimension 2.
method Optimal transport techniques.
result Sharpness of the inequality for submanifolds of codimension 2.
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.