Proposes a new distance metric for multi-marginal optimal transport.
problem Computational scalability in multi-marginal optimal transport.
method Random one-dimensional projections to construct sliced multi-marginal Wasserstein distance.
result Sliced multi-marginal Wasserstein distance is a metric with dimension-free sample complexity.
This paper tackles multi-marginal optimal transport problems using DC programming.
problem Multi-marginal optimal transport problems in machine learning.
method Promoting structural information in MMOT leads to a DC programming problem.
result Solutions from DC optimization are as qualitative as current methods.
The Skorokhod Embedding Problem (SEP) is one of the classical problems in the study of stochastic processes, with applications in many different fields (cf.~ the surveys \cite{Ob04,Ho11}). Many of these applications have natural multi-marginal extensions leading to the \emph{(optimal) multi-marginal Skorokhod problem} …
3MSBM learns smooth trajectories from multiple snapshots.
problem Capturing long-range temporal dependencies in complex systems.
method Lifts dynamics to phase space, generalizes stochastic bridges to multi-marginal conditional problems, learns transport maps preserving intermediate marginals.
result Significantly improves convergence and scalability in capturing complex dynamics.
MSBM extends SB for multi-marginal trajectory inference.
problem Trajectory inference from multiple discrete snapshots.
method Multi-Marginal Schrödinger Bridge Matching (MSBM) using iterative Markovian fitting (IMF).
result MSBM effectively captures complex trajectories and respects intermediate distributions.
Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this problem has two critical challenges: (i) Measuring the multi-marginal distance amon…
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.
Efficiently computes robust option prices using multi-marginal martingale transport.
problem Computing robust option prices under martingale constraints.
method Extending state space, sequential martingale structure, entropic regularisation.
result Fast computation of optimal solutions for large problems.
New algorithm for efficient inference over tree-structured graphs.
problem Inference over probabilistic graphical models with aggregate data.
method Optimal transport theory, Sinkhorn/iterative scaling algorithm, belief propagation.
result Global convergence and polynomial computational complexity.
A new algorithm reconstructs population dynamics from coarse samples.
problem Reconstructing population dynamics from unlabeled samples at coarse time intervals.
method Deep Momentum Multi-Marginal Schrödinger Bridge (DMSB) framework.
result Significantly outperforms baselines in synthetic and real-world datasets.
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed \emph{coarse scalar curvature}, generalizes a recent definition of Ricci curvature for…
A new algorithm estimates aggregate marginals from noisy data in an online manner.
problem Estimating aggregate marginals of a Markov chain from noisy aggregate observations.
method Sliding window Sinkhorn belief propagation (SW-SBP) algorithm.
result Demonstrated improved performance on inferring population flow.
TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.
problem Optimal transport with multiple marginals and tree-structured quadratic costs.
method Tree-based Diffusion Schrödinger Bridge (TreeDSB) for continuous and dynamic solutions.
result TreeDSB efficiently computes Wasserstein barycenters in high dimensions.
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of non-metrics can complicate solving them. Multi-marginal OT (MMOT) generalizes OT to si…
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). New method learns cell trajectories from multiple snapshots.
problem Inferring cell trajectories from limited, single-time-point data.
method Multi-marginal Schrödinger Bridges with iterative reference refinement.
result Effective in capturing long-term dependencies and learning from multiple time points.
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…
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.
Develops a new algorithm to calibrate signed datasets to specified marginals.
problem Calibrating signed datasets to specified marginals.
method Extends Schrödinger-Fortet-Sinkhorn paradigm to sign-indefinite multi-dimensional arrays.
result Proposes an optimization problem to update a sign-indefinite prior to match given marginals.
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network wi…
Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Sev…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretisation and linear programmin…
Framework learns continuous dynamics from sparse trajectories.
problem Learning dynamics from sparsely sampled and high-dimensional trajectories.
method Interpolative Multi-Marginal Flow Matching (IMMFM) framework.
result IMMFM outperforms existing methods in forecasting and downstream tasks.
We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we establish absolute continuity of the barycenter of general measures Ω∈P(P(M)) on Wasserstein space, extending on one hand, results in the Euclidean case (for ba…
Develops a method for fairness in multi-task learning using Wasserstein barycenters.
problem Extending fairness to multi-task learning with shared representations.
method Definition of Strong Demographic Parity extended to multi-task learning using multi-marginal Wasserstein barycenters. Closed form solution for optimal fair predictor.
result Empirical results show practical value of post-processing methodology in promoting fair decision-making.
Generative profiling improves real-time task timing for varied resource contexts.
problem Inaccurate task timing analysis for complex hardware architectures.
method Nonparametric, conditional multi-marginal Schrödinger Bridge (MSB) formulation for synthesizing context-dependent timing profiles.
result Maximum likelihood accurate execution profiles for unseen resource contexts.
The study connects fairness constraints with optimal transport to derive new insights in classification.
problem Ensuring fairness in classification models without sacrificing performance.
method Using Wasserstein barycenters and optimal transport, the study characterizes optimal classification functions under fairness constraints.
result Maximizing fairness under demographic parity is equivalent to solving a regression problem.
COTA learns abstraction maps from data without complete SCM knowledge.
problem Learning causally consistent representations at different resolutions.
method Multi-marginal Optimal Transport (OT) with do-calculus constraints and interventional cost.
result COTA outperforms non-causal and independent formulations on synthetic and real-world problems.
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
The paper examines how small positive dependence can lead to correlated tail risks.
problem Understanding the impact of dependence uncertainty on tail risk measures.
method Introducing a regular dependence measure and analyzing the aggregation of risks.
result Small positive dependence can result in perfectly correlated tail risks.
ACSSM models irregular time series with continuous dynamics.
problem Modeling irregular time series data.
method ACSSM uses a multi-marginal Doob's h-transform and variational inference with stochastic optimal control.
result ACSSM outperforms in tasks like classification, regression, interpolation, and extrapolation.
New method solves tree-structured Schrödinger Bridge problems.
problem Computing Schrödinger Bridge between tree-structured distributions.
method Iterative Markovian Fitting (IMF) procedure for tree-structured costs.
result Extends IMF to tree-structured Schrödinger Bridge problems.
New margin-based regularization and selective sampling improve deep neural network performance.
problem Improving deep neural network performance on various classification tasks.
method Multi-margin regularization (MMR) and minimal margin score (MMS) for selective sampling.
result Improved results on multiple classification tasks across domains.
Sliced Optimal Transport simplifies OT for fast computation.
problem Efficient computation of distances and barycenters for probability measures.
method Combines OT, integral geometry, and statistics for fast computation.
result Retains rich geometric structure while speeding up computations.
Proposes MFSWB for marginal fairness in SWB, improving efficiency and performance.
problem Achieving marginal fairness in SWB averaging.
method Defining MFSWB as a constrained SWB problem, proposing two surrogate problems and a new slicing distribution.
result Surrogate MFSWB problems effectively minimize distances to marginals and encourage marginal fairness.
Proposes a sequential framework for fairness in multiple sensitive attributes.
problem Fairness in the presence of multiple sensitive attributes.
method Sequential framework using multi-marginal Wasserstein barycenters.
result Closed-form solution for sequentially fair predictor.