A neural network speeds up computation of Wasserstein barycenters by 60x.
problem Computing Wasserstein barycenters is computationally demanding.
method Trained a deep convolutional neural network to compute Wasserstein barycenters.
result Computational times reduced from milliseconds to seconds.
New algorithm approximates continuous Wasserstein barycenters efficiently.
problem Computing Wasserstein barycenters for continuous distributions.
method Stochastic algorithm using dual potentials and stochastic gradient descent.
result Efficient online approximation of continuous Wasserstein barycenters.
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.
New algorithm computes optimal transport barycenter efficiently.
problem Computing optimal transport barycenter for high-dimensional probability distributions.
method Wasserstein-Descent H˙1-Ascent (WDHA) algorithm. result Exact barycenter computation in nearly linear time and linear space complexity.
A new algorithm computes Wasserstein barycenters without entropic regularization.
problem Computing Wasserstein barycenters efficiently and accurately.
method Free-support algorithm based on particle flow and Riemannian geometry.
result The algorithm avoids entropic regularization and is computationally tractable.
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.
Scalable algorithm for computing Wasserstein-2 barycenters without bias.
problem Computing Wasserstein-2 barycenters efficiently and accurately.
method Input convex neural networks and cycle-consistency regularization.
result Our approach avoids introducing bias and does not require minimax optimization.
Develops a method to efficiently compute Wasserstein barycenters with variational distributions.
problem High computational burden in computing Wasserstein barycenters for high-dimensional and continuous settings.
method Introduces a variational distribution to approximate the continuous Wasserstein barycenter, reformulating the problem as an optimization with c-cyclical monotonicity.
result The method provides a tractable dual formulation for efficient computation of Wasserstein barycenters, demonstrated on real applications.
First DP algorithm for Wasserstein barycenters on private data.
problem Computing Wasserstein barycenters on private datasets.
method Differentially private algorithms for Wasserstein barycenters.
result High-quality private barycenters with strong accuracy-privacy tradeoffs.
A scalable algorithm approximates Wasserstein Barycenters using neural networks.
problem Representing the weighted mean of probability distributions in high dimensions.
method Input Convex Neural Networks (ICNNs) for Kantorovich dual formulation of Wasserstein-2 distance.
result Generative model representation of the Barycenter with infinite samples.
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
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.
Paper introduces SGA for barycenter optimization in optimal transport.
problem Optimizing Wasserstein barycenter for discrete distributions.
method Sobolev gradient ascent algorithm tailored to Wasserstein geometry.
result SGA achieves convergence rate similar to subgradient descent.
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances to each element in that set. We propose two original algorithms to compute Wasse…
New method for scalable barycenter computation using Wasserstein gradient flows.
problem Scalability and integration of label information in barycenter computation.
method Gradient flows in Wasserstein space, time discretization, mini-batch optimal transport, modular regularization, task-aware functions, supervised information integration.
result Empirically validated new state-of-the-art barycenter solver with labeled barycenters outperforming unlabeled ones.
A new method for barycenter of probability measures using entropic optimal transport.
problem Finding a weighted average of probability distributions.
method Doubly regularized Wasserstein barycenters with entropic optimal transport.
result The new formulation is debiased and has a smooth density, leading to efficient estimation and optimization.
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.
Debiased Wasserstein barycenters improve on entropy regularization in OT.
problem Entropy regularization in OT introduces bias, leading to blurred barycenters.
method Propose debiased Wasserstein barycenters using Sinkhorn iterations.
result Debiased barycenters preserve fast Sinkhorn-like iterations without entropy smoothing bias.
New method synthesizes and analyzes probability measures using entropy-regularized optimal transport.
problem Synthesize and analyze probability measures with entropy-regularized optimal transport.
method Entropy-regularized Wasserstein-2 cost and Sinkhorn divergence for synthesis and analysis.
result Computed barycentric coefficients and their stability for classification of corrupted point cloud data.
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.
Study absolute continuity of Wasserstein barycenters on manifolds with singular cost functions.
problem Absolute continuity of Wasserstein barycenters on manifolds with singular cost functions.
method Approximation framework to handle singularity, geometrically transparent.
result Precise analytic condition on cost profile for necessary assumptions.
In this paper we propose to perform model ensembling in a multiclass or a multilabel learning setting using Wasserstein (W.) barycenters. Optimal transport metrics, such as the Wasserstein distance, allow incorporating semantic side information such as word embeddings. Using W. barycenters to find the consensus between…
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such at…
Proposes using Wasserstein barycenter for better multilingual alignment.
problem Finding word-to-word translations between multiple languages without parallel data.
method Uses Wasserstein barycenter as a more informative pivot language, minimizing pairwise transportation costs.
result Demonstrates state-of-the-art performances on standard benchmarks.
Paper introduces a novel framework for supervised graph prediction using Optimal Transport.
problem Supervised labeled graph prediction.
method Fused Gromov-Wasserstein (FGW) loss and FGW barycenter with neural network weights and learned graphs.
result The method can interpolate in the labeled graph space and achieve good performance on difficult problems.
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the…
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.
The paper develops a method to achieve fairness in predictions using Wasserstein barycenters.
problem Learning a fair real-valued function independent of sensitive attributes.
method Establishing a connection between fair regression and optimal transport theory, deriving a close form expression for the optimal fair predictor as the Wasserstein barycenter of sensitive groups.
result The optimal fair predictor's distribution is the Wasserstein barycenter of sensitive groups' distributions, offering an intuitive interpretation and a simple post-processing algorithm.
Spectral clustering improves accuracy and efficiency for clustering discrete distributions.
problem Inaccurate clustering of discrete distributions using traditional methods.
method Spectral clustering combined with distribution affinity measures (MMD, Wasserstein distance) and linear optimal transport.
result Spectral clustering outperforms traditional methods in accuracy and efficiency.
We propose Gaussian optimal transport for Image style transfer in an Encoder/Decoder framework. Optimal transport for Gaussian measures has closed forms Monge mappings from source to target distributions. Moreover interpolates between a content and a style image can be seen as geodesics in the Wasserstein Geometry. Usi…
Generative model improved using Liouville PDE-based sliced-Wasserstein flow.
problem Improving generative models for fair regression.
method Transformed sliced-Wasserstein flow into Liouville PDE-based formalism, handling density estimation with normalizing flows of neural ODE.
result Outperforms in convergence and fairness with reduced variance.
A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.
problem Learning principal variations of random probability measures under Wasserstein geometry.
method Introducing a new dynamical formulation of log-PCA as a variational approach.
result Deriving a general statistical convergence rate for empirical WT-PCA.
New clustering method for uncertain data using Wasserstein barycenters.
problem Clustering uncertain and structured data with observational/experimental error.
method Wasserstein barycenters and geodesic criterion for optimal clustering.
result Effective clustering of complex data in astronomy, biology, and remote sensing.
We introduce a weak notion of barycenter of a probability measure μ on a metric measure space (X,d,m), with the metric d and reference measure m. Under the assumption that optimal transport plans are given by mappings, we prove that our barycenter B(μ) is well defined; it is a probability measur…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map. Although some algorithms have been proposed to learn this map, they rely on kernel-ba…
A novel unsupervised domain adaptation method using hierarchical optimal transport.
problem Unsupervised domain adaptation between source and target domains.
method Hierarchical optimal transport, leveraging class labels for structure formation in the source domain and learning probability measures in the target domain.
result The proposed HOT-DA method outperforms state-of-the-art approaches on various datasets.
A new method for computing shape barycenters from point clouds using Procrustes-Wasserstein distance.
problem Computing representative shapes from point clouds with precise alignment and shape preservation.
method Developed a new distance metric (Procrustes-Wasserstein) and algorithms for computing barycenters.
result Superior performance in precise alignment and shape preservation compared to existing OT approaches.
Develops a new model for synthesizing and analyzing probability measures.
problem Synthesis and analysis of probability measures.
method Linear barycentric coding model (LBCM) using linear optimal transport (LOT) metric.
result Closed-form solution to 2-Wasserstein barycenters for compatible measures.
We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first show how this estimator, termed Bayesian Wasserstein barycenter (BWB), arises na…
New metrics compare rational spectra using optimal transport.
problem Comparing rational spectra efficiently and accurately.
method Optimal transport and linear-systems theory.
result Established connection to Wasserstein distance.
A JAX toolbox solves optimal transport problems for point clouds and histograms.
problem Optimal transport problems between point clouds and histograms.
method Automatic and custom reverse mode differentiation, vectorization, just-in-time compilation, and accelerators support.
result Solves a wide range of optimal transport problems including regularized OT, barycenters, Gromov-Wasserstein, and low-rank solvers.
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various probability measures, as in the Wasserstein barycenter problem, or to carry out param…
Proposes using Wasserstein barycenters for robust optimization with multiple data sources.
problem Distributionally robust optimization with multiple heterogeneous data sources.
method Construct nominal distribution through Wasserstein barycenter of multiple data samples, reformulates as a finite convex program.
result Proposed scheme outperforms other estimators in sparse inverse covariance matrix estimation.
The paper proposes a method to ensure fairness in machine learning models.
problem Ensuring fairness in machine learning models powered by supervised learning.
method Optimal affine transport and Wasserstein-2 barycenter to characterize the Pareto frontier between prediction error and statistical disparity.
result The proposed method effectively balances prediction accuracy and fairness, as demonstrated by numerical simulations.
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons: sensors in a sensor network may be placed far apart, affecting their individual meas…
New geometry for optimal transport cost based on Bregman divergences.
problem Optimal transport cost calculation with Bregman divergences.
method Established properties, defined interpolations, constructed dualistic geometry.
result Derived generalized Pythagorean inequality and Bregman-Wasserstein barycenters.
New DG method minimizes barycentric alignment and reconstruction loss.
problem Improving domain generalization in machine learning.
method Introduces a new upper bound and WBAE algorithm.
result WBAE outperforms state-of-the-art DG algorithms.
We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual algorithms and their capability in solving other problems in large-scale, such …