A new variational inference method using optimal transport.
problem Approximating complex posterior distributions with flexible particle-based methods.
method Introducing a new particle-based variational inference method based on semi-discrete optimal transport.
result The method provides a particle approximation and optimal transportation densities.
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.
This paper uses normalizing flows to approximate transport maps between densities.
problem Approximating transport maps between given densities.
method Construct time-dependent controls using normalizing flows.
result Provides bounds on the number of switches for piecewise constant approximations.
A fast and practical method for learning transport maps.
problem Slow and computationally expensive methods for learning transport maps.
method Approximated transport mapping using Gaussian (Bures-Wasserstein) transport and local transport plans.
result Significantly faster and more efficient than existing methods.
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.
Paper tackles robust optimal transport with improved computational complexity and barycenter approximation.
problem Computing robust optimal transport and its barycenter efficiently.
method Sinkhorn-based algorithms for robust optimal transport and iterative Bregman projections for barycenter approximation.
result Improved computational complexity for robust optimal transport and barycenter approximation.
Paper establishes rates of universal approximation for neural tangent kernels using transport mappings.
problem Universal approximation for neural tangent kernels with microscopic weight changes.
method Generic scheme to approximate functions with NTK using transport mappings, constructed via Fourier transforms.
result Approximation of continuous functions with roughly 1 / δ^(10d) nodes, where δ depends on function continuity.
Paper shows near-linear time approximation for optimal transport.
problem Computing optimal transport distances efficiently.
method New analysis of Sinkhorn iteration and greedy coordinate descent algorithm, Greenkhorn.
result Achieves near-linear time approximation for optimal transport distances.
A new method for mini-batch optimal transport improves scalability and accuracy.
problem Desired estimation and proper metric approximation in m-OT.
method BoMb-OT: Finds optimal coupling between mini-batches.
result BoMb-OT approximates a proper metric and improves m-OT's performance.
A practical algorithm improves approximate OT distances using quantization.
problem Substantial computational burden in computing OT distances for large samples.
method Introduces a quantization step to estimate OT distances between measures.
result The quantization step improves the performance of approximate solvers for entropy-regularized transport.
The paper tackles efficient computation of optimal transport by approximating conjugates with amortized optimization.
problem Efficient computation of convex conjugates in optimal transport is challenging and limits the quality of transport maps.
method The approach combines amortized approximations of conjugates with a fine-tuning solver to improve transport map quality.
result The method significantly improves the quality of transport maps for the Wasserstein-2 benchmark and models many 2D couplings and flows.
A new method improves Bayesian filtering in nonlinear systems.
problem Bayesian filtering in nonlinear dynamical systems with non-Gaussian posteriors.
method Transport maps with block-triangular structure and gradient flows for MMD minimization.
result Accurate approximation of non-Gaussian posteriors without particle collapse.
Paper generalizes tensor-train approximation for complex random variables.
problem Characterizing intractable high-dimensional random variables.
method Extends inverse Rosenblatt transform to general reference measures and integrates into deep variable transformation framework.
result Deep inverse Rosenblatt transport significantly expands tensor approximations for complex random variables.
TSC uses HMC and adaptive transport maps to optimize forward KL for variational inference.
problem Variational inference underestimates uncertainty when minimizing reverse KL.
method TSC uses Hamiltonian Monte Carlo and adaptive transport maps to optimize KL(p||q).
result TSC achieves competitive performance in training variational autoencoders on large-scale data.
The paper introduces regularized OT to create sparse transportation plans.
problem Lack of sparsity in entropic regularization of OT.
method Regularizing primal and dual OT formulations with strongly convex terms, leading to sparse transportation plans.
result Regularized OT can lead to sparser transportation plans than entropic regularization.
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.
Two log-linear approximations speed up optimal transport for deep learning applications.
problem Computing optimal transport in high dimensions is computationally expensive.
method Locality-sensitive hashing (LSH) and Nyström approximation with LSH-based sparse corrections.
result Log-linear time algorithms for entropy-regularized OT perform well in high-dimensional spaces.
SOS programming verifies MTW tensor non-negativity for optimal transport maps.
problem Verifying MTW tensor non-negativity for general cost functions is difficult.
method Sum-of-Squares (SOS) programming for verifying and approximating MTW non-negativity.
result SOS programming provides certificates and approximations of MTW non-negativity.
Discriminator optimizes to approximate optimal transport for better image generation.
problem Improving the quality of generated images using GANs.
method Trains discriminator to optimize a lower bound of Wasserstein distance, approximating optimal transport.
result Trained discriminator improves inception score and FID metrics.
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.
A new method uses normalizing flows to approximate optimal transport between empirical distributions.
problem Learning an optimal transport map between two empirical distributions.
method Relaxing the Monge formulation of optimal transport, using normalizing flows to approximate the solution.
result The method provides a good approximation of the true optimal transport.
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).
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.
Bi-Lipschitz flows approximate a wide range of distributions.
problem Characterizing the expressivity of bi-Lipschitz normalizing flows.
method Linking score regularity to transport map bi-Lipschitzness via probability flow ODE.
result Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are L1-dense among all probability densities. 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.
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 schedules improve transport map approximation and learning.
problem Improving the approximation and learning of transport maps.
method Optimal scheduling of transport maps to minimize spatial Lipschitz constant.
result The optimal schedule can be computed in closed form and results in a significantly smaller Lipschitz constant.
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.
This paper develops a scalable Thompson Sampling method using optimal transport.
problem Efficiently approximating posterior distributions for complex models in Thompson Sampling.
method The approach uses distribution optimization techniques via Wasserstein gradient flows to approximate posterior distributions efficiently.
result The proposed method achieves superior performance on both synthetic and real large-scale data.
A new algorithm screens negligible components to efficiently approximate optimal transport distances.
problem Efficiently approximating the Sinkhorn distance between discrete measures.
method Screening of negligible components in the dual solution of the regularized Sinkhorn problem.
result Screenkhorn algorithm provides provable guarantees with smaller computational complexity.
Transformer models align words through attention weights, closely approximating Optimal Transport.
problem Understanding the internal mechanism of transformer models in language processing.
method Empirical evidence and theoretical analysis of attention weights and their relation to Optimal Transport.
result Transformer models can simulate gradient descent on the dual of entropy-regularized OT problem, providing a theoretical foundation for token alignment.
Framework approximates 2-Wasserstein distance for GANs training.
problem Training GANs with improved metrics and analysis.
method Approximates 2-Wasserstein distance via restricted convex potentials.
result Improved training for GANs with moment-matching property.
This work relaxes OT problems with marginal moments constraints, achieving finite discrete measures.
problem Solving Optimal Transport problems with marginal moments constraints.
method Relaxation of OT problems using moment constraints and Tchakaloff's theorem.
result The Moment Constrained Optimal Transport problem (MCOT) is achieved by a finite discrete measure.
This paper develops optimal transport methods on the roto-translation group SE2.
problem Optimal transport on the roto-translation group SE2 for image analysis.
method Develops a computational framework for optimal transportation over Lie groups, focusing on SE2. Uses Sinkhorn-like algorithm with efficient distance approximations.
result Advances in image barycentric interpolation, orientation field interpolation, and Wasserstein flows on SE2.
New algorithm approximates optimal transport cost with additive error in near-linear time.
problem Scalable approximation of optimal transport cost with additive error.
method Adapted classical graph algorithm of Gabow and Tarjan, with novel analysis.
result Achieves execution time of $O( rac{n^2 C}{δ} + rac{nC^2}{δ^2})$.
This work explains GAN mode collapse and convergence issues via optimal transportation theory.
problem GANs struggle with convergence and mode collapse due to discontinuous optimal transportation mappings.
method The study connects GANs to optimal transportation theory, testing hypotheses about discontinuity and proposing a new method to approximate continuous Brenier potentials.
result The supports of real data distributions are often non-convex, leading to discontinuous optimal transportation mappings and mode collapse in GANs.
A new framework for generative modeling using value-driven transport.
problem Developing efficient methods for generative modeling.
method A discrete-time stochastic control formulation of measure transport, formulated as a linear program with dual variables corresponding to the optimal value function.
result Well-trained VDT policies lead to straight transport paths that can be simulated quickly and robustly.
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
Explains linearizing a nonlinear connection on a pullback bundle.
problem Clarifying the geometric meaning of linearized connections.
method Fiberwise linear approximation of a vector bundle connection.
result Clarifies the geometric meaning of linearized connections.
New method uses SoS densities and α-divergences for efficient sequential transport maps.
problem Efficiently generating samples from approximated densities.
method Sequential transport maps using Sum-of-Squares (SoS) densities and α-divergences.
result Convex optimization problems with efficient semidefinite programming solutions.
Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.
problem Graph Neural Networks (GNN) often lose structural or semantic information when aggregating node embeddings.
method Combines optimal transport (OT) with parametric graph models to compute graph embeddings from Wasserstein distances between node embeddings and prototype point clouds.
result OT-GNN outperforms popular methods on molecular property prediction tasks and produces smoother graph representations.
Sliced-regularized OT improves transport plan accuracy.
problem Optimal transport (OT) approximation accuracy.
method Sliced-regularized optimal transport (SROT) formulation.
result SROT yields more accurate approximations of exact OT than entropic OT.
Geometrically reformulates the Laplace method for optimal transport.
problem Approximating integrals using the Laplace method without geometric interpretation.
method Introduces the Kim-McCann Riemannian metric to give a geometric formulation of the Laplace method.
result Expresses the first-order term of the Laplace method using geometric objects.
Develops methods for structured variational inference with star-structured models.
problem Inference in models with interdependent variables.
method Star-structured variational inference, existence, uniqueness, self-consistency proofs, approximation error bounds, gradient-based algorithm.
result First results for existence, uniqueness, and self-consistency of variational approximations in star-structured models.
New algorithm solves online resource allocation problems efficiently.
problem Dynamic resource allocation in operations research.
method Minimal Selection Principle and MSoE algorithm.
result Ensures optimal cumulative regret bounds in dynamic resource allocation.
SVGD uses particle transport to approximate distributions, with theoretical guarantees.
problem Approximating complex distributions efficiently.
method Iterative particle transport guided by gradient of KL divergence.
result SVGD's asymptotic behavior is a gradient flow under a new metric.
New algorithms for approximating multimarginal optimal transport with near-linear time complexity.
problem Approximating the multimarginal optimal transport distance between multiple discrete probability distributions.
method Proposed two deterministic algorithms: multimarginal Sinkhorn and accelerated multimarginal Sinkhorn, achieving near-linear time complexity.
result Achieved near-linear time complexity bounds for approximating the MOT problem, matching best known bounds for classical OT.
New research shows SAA can outperform SA for Wasserstein barycenters.
problem Optimizing Wasserstein barycenters with entropy regularization.
method Comparison of Stochastic Approximation (SA) and Sample Average Approximation (SAA) for large-scale problems.
result SAA can be more efficient than SA for Wasserstein barycenters, especially in large-scale settings.