Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
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.
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.
A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
problem Testing conditional independence between two random vectors given a third.
method Constructing transport maps to transform conditional independence into unconditional independence, estimating these maps from data using conditional continuous normalizing flow models.
result The proposed method is validated through simulations and real-data analysis, demonstrating practical effectiveness.
This paper proposes a new method for conditional sampling using optimal transport.
problem Sampling conditional distributions in Bayesian inference and density estimation.
method Iterative block-triangular transport maps solving an optimal transport problem with a weighted L2 cost function.
result The proposed method extends the data-driven approach for conditional sampling.
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…
Study optimal transport on null hypersurfaces and null energy condition.
problem Optimal transport degeneracy on null hypersurfaces.
method Developed tools to characterize null energy condition using convexity properties of entropy.
result Optimal transport characterization of null energy condition.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "conn…
Estimates conditional Brenier maps using entropic optimal transport.
problem Non-parametric estimation of conditional Brenier maps.
method Entropic optimal transport for scalable non-parametric estimation.
result Entropic optimal transport maps asymptotically converge to conditional Brenier maps.
Efficiently computes optimal transport maps and Wasserstein barycenters using conditional normalizing flows.
problem Computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces.
method Uses conditional normalizing flows to approximate distributions and solve the primal problem.
result Shows computational feasibility for hundreds of input distributions and yields accurate results.
Method learns conditional distributions using neural entropic optimal transport.
problem Challenges in learning multiple conditional distributions.
method Neural entropic optimal transport method with two networks and regularization.
result Effective learning of conditional distributions with limited samples.
New method for conditional sampling using M-GANs, likely-free inference.
problem Conditional sampling of probability measures.
method Developed a novel computational approach called M-GANs based on block triangular transport.
result Accurate sampling of conditional measures in various applications.
Improves QMC for complex distributions using transport maps.
problem Challenges in applying QMC to general target distributions.
method Train a transport map to approximate target distributions, ensuring RQMC achieves superior error rates.
result Transport QMC achieves faster convergence rates than standard Monte Carlo under mild conditions.
New framework for conditional risk minimization using optimal transport.
problem High-stakes decisions with side information, especially economic conditions.
method Universal framework based on union-ball formulation in optimal transport.
result Offers interpretability, tractability, and scalability for various risk functionals.
Biholomorphisms of transport twistor spaces are rigid under certain conditions.
problem Rigidity of biholomorphisms in transport twistor spaces.
method Proof of rigidity for biholomorphisms between transport twistor spaces of simple or Anosov surfaces.
result Biholomorphisms are rigid, up to constant rescaling and the antipodal map, being lifts of orientation-preserving isometries.
New methods target conditional demographic parity using optimal transport distances.
problem Auditing and enforcing conditional demographic parity (CDP) in models with complex conditioning variables.
method Developed novel measures of conditional demographic disparity (CDD) based on optimal transport distances and regularization-based approaches.
result Validated methods airbit{} and airlp{} effectively target CDP in real-world datasets with continuous model outputs.
The study characterizes straight-line flows in dynamic measure transport.
problem Tackles the challenge of designing flows that are easy to integrate.
method Characterizes straight-line flows using a PDE and Reynolds tensor.
result Characterizes affine-in-time interpolants and necessary conditions for flow geometry.
Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
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. This work clarifies different transport map constructions and their causal interpretations.
problem Identifying distinct transport map constructions and their equivalence.
method Comparative analysis of three transport map constructions: cyclically monotone, quantile-preserving, and triangular monotone.
result Conditions for equivalence of different transport map constructions.
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.
Optimal algorithms for Riemannian optimization with reduced complexity.
problem Stochastic optimization on Riemannian manifolds with limited data.
method Zeroth-order Riemannian Averaging Stochastic Approximation algorithms using Riemannian moving-average estimators and novel geometric conditions.
result Achieves optimal sample complexities for generating approximate first-order stationary solutions.
This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability measures characterizes lower bounds of the Ricci curvature. We then discuss geometric properties of general metric measure …
Extends geostatistical simulation method to handle multiple variables and large grids.
problem Scalability and handling of multiple variables in geostatistical simulation.
method Uses Sinkhorn optimal transport with sparse matcher and FFT-MA Gaussian backbone.
result MST-Direct reproduces joint distribution with zero histogram error and accurately preserves spatial correlation.
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.
New method uses kernel Stein discrepancy for measure transport without strict continuity constraints.
problem Minimizing Kullback-Leibler divergence for posterior approximation.
method Proposes minimizing kernel Stein discrepancy instead of Kullback-Leibler divergence.
result Demonstrates consistency and competitiveness of the new method.
Two probability distributions μ and ν in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are al…
Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.
problem Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
method Develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
result The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss.
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the first time in 4-dimensional Euclidean space. Then we obtain the conditio…
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. 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…
New findings show different cost functions yield equivalent curvature bounds.
problem Establishing equivalence of curvature bounds under various transport costs.
method Needle decomposition and localization technique for optimal transport.
result All CDp(K,N) conditions are equivalent for p>1. Optimal transport aligns source and target distributions for domain adaptation.
problem Unsupervised domain adaptation with joint class-conditional and label shifts.
method Minimizes importance weighted loss and Wasserstein distance for aligned marginals and class-conditional distributions.
result Our method outperforms competitors on various domain adaptation tasks.
New framework uses cohomology to analyze probabilistic distortions and arbitrage.
problem Analyzing probabilistic distortions and arbitrage in categorical filtrations.
method Transport cohomological framework, simplicial structure, loop effects, holonomy.
result Nontrivial probabilistic distortions and obstructions generated by loops.
A new copula model for multi-attribute data using optimal transport.
problem Relaxing the Gaussian assumption for multi-attribute graphical models.
method Introducing a new copula (Cyclically Monotone Copula) and using optimal transport theory.
result The model allows arbitrary continuous distributions and is more flexible than classical methods.
Develops regularity theory for Beckmann's optimal transport problem.
problem Minimizing total squared flux in continuous transport from source to target.
method Unconstrained Lagrangian formulation, variational first order optimality conditions, Schauder estimates.
result Exact Hölder regularity of potential, flux, and flow generating on bounded, regular domains.
Unified framework for efficient trans-dimensional Bayesian inference using VI and NFs.
problem Efficient trans-dimensional Bayesian inference with reduced computational cost.
method Variational inference with normalizing flows to train transport proposals.
result Our approach minimizes reverse KL divergence and reduces computational cost.
Efficiently learns and transports posterior densities for real-time inference.
problem High computational cost of Bayesian inference for complex posterior densities.
method Tensor-train (TT) format for offline learning, conditional transport for online inference.
result Significant improvement in inference performance for high-dimensional problems.
A new method for conditional sampling using paired Wasserstein Autoencoders.
problem Conditional sampling from complex data distributions.
method Derive a novel loss function for Wasserstein Autoencoders to enable sampling from OT-type couplings.
result Learned cost-optimal transport maps and conditional sampling from an OT-type coupling.
Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution p and the generator distribution pG. It implies that the trained discriminator can approximate opti…
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.
Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed by positivity of sectional curvature.
Integrates side information for robust portfolio optimization.
problem Portfolio optimization under uncertainty and side information.
method Distributionally robust optimization with optimal transport ambiguity set.
result The problem can be reformulated as a finite-dimensional optimization problem.
Two neural network methods approximate conditional optimal transport for Bayesian inference.
problem Approximating conditional optimal transport for Bayesian inference in high dimensions.
method Neural network approximations of conditional optimal transport maps.
result Improved scalability and modeling choices for conditional sampling and density estimation.
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…
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.
Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on …