Adapts DR objectives for both sample and feature size reduction.
problem Simultaneously reduce sample and feature sizes.
method Semi-relaxed Gromov-Wasserstein optimal transport.
result OT plan delivers competitive hard clustering.
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48 results for “semi-relaxed OT”
New algorithm for low-rank optimal transport with improved interpretability and efficiency.
problem Quadratic scaling of optimal transport coupling matrix for massive datasets.
method Factor Relaxation with Latent Coupling (FRLC) algorithm.
result Superior performance on diverse applications including graph clustering and spatial transcriptomics.
A new method for efficient inference and model selection in SBMs using OT.
problem Efficient inference and model selection in stochastic block models.
method Interpreting MLVI as srGW with entropic regularization, then unregularizing for sparse solutions, and adding a sparsity-promoting regularizer.
result The method consistently recovers SBM parameters and selects the number of clusters in finite samples.
Efficiently predicts optimal transport plans using sliced potentials.
problem Predicting optimal transport plans across multiple measure pairs efficiently.
method Regression-based and objective-based amortization strategies using sliced optimal transport potentials.
result Efficient and accurate prediction of optimal transport plans for various tasks.
New method uses continuous OT for fairness, outperforming discrete OT.
problem Fairness issues in machine learning models.
method Stochastic-gradient fairness method based on continuous optimal transport.
result Continuous OT method outperforms discrete OT when data is limited.
Super-OT combines GANs and optimal transport for lineage tracing.
problem Lineage tracing in single-cell RNA-seq data.
method Supervised learning framework with GANs for optimal transport.
result Super-OT outperforms Waddington-OT in predicting cell differentiation outcomes.
Riemannian Neural OT maps improve scalability on manifolds.
problem Challenges in extending neural OT to high-dimensional Riemannian manifolds.
method Introduces Riemannian Neural OT (RNOT) maps that avoid discretization and incorporate geometric structure.
result RNOT maps approximate Riemannian OT maps with sub-exponential complexity in the dimension.
Meta Optimal Transport learns from past problems to solve similar OT problems faster.
problem Solving similar optimal transport problems repeatedly from scratch is inefficient.
method Amortized optimization to predict optimal transport maps from past solutions.
result Meta OT models can solve new problems faster than standard methods.
Review of unbalanced OT, entropic regularization, and GW for robust data comparison.
problem Lack of robustness, high computational costs, and difficulty in handling distinct spaces in OT.
method Unbalanced OT, entropic regularization, Gromov-Wasserstein distance.
result Efficient geometric loss functions for data sciences.
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.
Paper solves inverse optimal transport problem with convex optimization and neural network.
problem Learning the cost function for optimal transport from observed data.
method Unconstrained convex optimization, Sinkhorn-Knopp algorithm, and deep neural network parameterization.
result Novel framework avoids repeated OT solving, demonstrating efficiency and accuracy.
Rapidly growing product lines and services require a finer-granularity forecast that considers geographic locales. However the open question remains, how to assess the quality of a spatio-temporal forecast? In this manuscript we introduce a metric to evaluate spatio-temporal forecasts. This metric is based on an Opti- …
Bispectral OT improves dataset comparison by preserving intrinsic coherence.
problem Ignoring intrinsic coherence in dataset comparisons using pairwise geometric distances.
method Introduces Bispectral Optimal Transport, a symmetry-aware extension of discrete OT.
result Transport plans computed with Bispectral OT achieve greater class preservation accuracy.
Study statistical guarantees for DRO with OT and OT-regularized divergences.
problem Enhancing adversarial robustness in machine learning models.
method Derive concentration inequalities for supervised learning via DRO-based adversarial training.
result First to cover soft-constraint costs and reweighting mechanisms in adversarial training.
New interpretation of OT regularization as adversarial ground cost.
problem Optimal transport (OT) regularization for machine learning.
method Using Fenchel duality, interpret convex OT regularization as adversarial ground cost.
result Access to a robust dissimilarity measure on the ground space.
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.
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.
New toolkit for directed distances improves flexibility of OT problems.
problem Optimal transport problems with constraints.
method Directed distances between quantile functions.
result Flexibility in solving OT problems enhanced.
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.
A new method computes high-dimensional optimal transport using flow neural networks.
problem Computing optimal transport for high-dimensional data.
method Optimizing a flow model to minimize transport cost between two arbitrary distributions.
result Trained optimal transport flow enables downstream tasks like DRE and domain adaptation.
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.
Optimizes optimal transport distances using low-dimensional embeddings.
problem High computational cost of optimal transport distances in high dimensions.
method Approximate OT distances using 1-Lipschitz maps in a lower-dimensional space.
result Efficiently approximates optimal transport distances with lower computational cost.
Modified Hungarian algorithm solves special OT problems efficiently.
problem Computing empirical Wasserstein distance in independence tests.
method Modified Hungarian algorithm for special OT problems.
result The modified algorithm solves special OT problems with complexity .
We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlying number field. This does not solve the open question whether the geometry of the OT manifold sees the class number directly, but brings us…
New algorithm improves OT map estimation for semi-discrete settings.
problem Improving estimation of OT maps in semi-discrete settings.
method Stochastic Gradient Descent with adaptive entropic regularization and averaging acceleration.
result Achieves nearly minimax rate of for OT map estimation.
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions. To that end, we propose a stochastic dual approach of regularize…
A new method combines energy-based models and entropy-regularized optimal transport.
problem Combining energy-based models and optimal transport for generative modeling.
method Energy-guided Entropic Neural Optimal Transport (E-ENT)
result Proves generalization bounds and validates scalability in image translation.
Transformers for Tabular Data: A Training Perspective of Self-Attention via Optimal Transportstat.ML
A study on optimizing self-attention in tabular data using Optimal Transport.
problem Improving efficiency and accuracy of self-attention in tabular classification tasks.
method Developed an OT-based algorithm to generate class-specific dummy Gaussian distributions and train an MLP.
result Achieved comparable accuracy to Transformers with reduced computational cost and efficiency.
Estimates optimal transport maps with known cost functions.
problem Ensuring optimal transport maps correspond to real-world usefulness.
method Differentiable neural ground costs with known Monge map forms.
result General approach for incorporating prior information.
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.
New online method estimates OT distances from sample streams.
problem Computing OT distances between arbitrary distributions.
method Online Sinkhorn algorithm using iterative enrichment of non-parametric representation.
result Consistent estimation of true regularized OT distance with nearly-O(1/n) sample complexity.
A new approach to denoising using optimal transport theory.
problem Improving latent variable recovery from noisy observations.
method Inspired by optimal transport theory, a new denoising method is developed.
result The new denoising method can recover latent variables from marginal distributions and posterior means.
OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.
problem Computational challenges in continuous normalizing flows.
method OT-Flow leverages optimal transport to regularize CNFs and uses exact trace computation.
result OT-Flow achieves competitive performance with one-fourth the number of weights and significant speedups.
A new method for flow matching reduces computational costs and improves performance.
problem Efficiently matching flow models to target data distributions.
method Semidiscrete formulation of optimal transport (SD-OT) using SGD and maximum inner product search (MIPS).
result Semidiscrete FM (SD-FM) outperforms batch-OT and traditional flow matching methods.
A new method for efficient optimal partial transport in 1D.
problem Limitation of equal mass assumption in optimal transport.
method Sliced Optimal Partial Transport (Sliced-OPT) algorithm.
result Sliced-OPT demonstrates computational and accuracy benefits.
New type of ruled surfaces studied with properties and examples.
problem Characterizing and understanding new types of ruled surfaces.
method Definition of a new orthonormal frame, calculation of Gaussian and mean curvatures, analysis of Weingarten map and geodesic properties.
result Conditions for an OT-surface to be flat or minimal are derived, and examples of helices and slant helices are provided.
This paper uses UOT metrics for better dimensionality reduction and classification/clustering.
problem Improving dimensionality reduction and classification/clustering methods.
method Uses Hellinger--Kantorovich metric from unbalanced optimal transport (UOT).
result UOT outperforms Euclidean and OT-based methods in classification and clustering tasks.
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some mome…
A form of generalisation error known as Off Training Set (OTS) error was recently introduced in [Wolpert, 1996b], along with a theorem showing that small training set error does not guarantee small OTS error, unless assumptions are made about the target function. Here it is shown that the applicability of this theorem …
New method for robustly estimating barycenters in data aggregation.
problem Outliers and noise in data measures hinder traditional OT barycenter estimation.
method Proposes a novel scalable approach using semi-unbalanced neural optimal transport.
result Demonstrates robustness to outliers and class imbalance.
The Oeljeklaus-Toma (OT-) manifolds are complex manifolds constructed by Oeljeklaus and Toma from certain number fields, and generalizing the Inoue surfaces . On each OT-manifold we construct a holomorphic line bundle with semipositive curvature form and trivial Chern class. Using this form, we prove that the OT-m…
Characterizes pluriclosed metrics on Oeljeklaus-Toma manifolds.
problem Characterizing existence of pluriclosed metrics on OT manifolds.
method Purely number-theoretical conditions.
result Explicit examples of pluriclosed OT manifolds in arbitrary complex dimension.
In this sequel, employing more commutative algebra than that explored in \cite{CCJ}, we show that an isoparametric hypersurface with four principal curvatures and multiplicities in is one constructed by Ozeki-Takeuchi \cite[I]{OT} and Ferus-Karcher-Münzner \cite{FKM}, referred to collectively as of OT-…
A new probabilistic framework for optimal transport using collective graphical models.
problem Measuring similarity between probability distributions and histograms.
method Probabilistic Optimal Transport based on Collective Graphical Models.
result OT with entropic regularization is equivalent to maximizing a posterior probability of a CGM.
Proposes m-POT to improve m-OT's misspecified mappings issue.
problem Misspecified mappings in mini-batch optimal transport.
method Partial optimal transport (POT) between mini-batch empirical measures.
result m-POT alleviates incorrect mappings compared to current methods.
CT-OT Flow estimates continuous-time dynamics from discrete snapshots.
problem Estimating continuous-time dynamics from temporally aggregated snapshots with noisy or uncertain timestamps.
method Two-stage framework: aligning neighboring intervals via partial optimal transport (POT) and reconstructing a continuous-time distribution through temporal kernel smoothing.
result Reduces distributional and trajectory errors compared with existing methods across synthetic and real datasets.
Study robust distribution estimation with Wasserstein distance, achieving optimal risk.
problem Robust distribution estimation under adversarial corruption.
method Combining partial OT and minimum distance estimation, proving structural properties and deriving a novel dual form.
result Achieves minimax-optimal robust estimation risk in many settings.
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.