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.
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.
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.
Optimal transport with path constraints for distributions of different masses.
problem Comparing distributions with different total masses under path constraints.
method Introduces a model for unbalanced optimal transport with path constraints, proving existence of solutions.
result Existence of solutions to path constrained unbalanced optimal transport for various constraints.
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.
We extend Sobolev transport to unbalanced measures on graphs.
problem Optimal transport struggles with measures of different total mass and high computational complexity.
method We propose a scalable unbalanced Sobolev transport (UST) for measures on graphs.
result UST admits a closed-form formula for fast computation and is negative definite.
Unbalanced COOT improves feature alignment robustly to outliers.
problem Optimal transport methods are sensitive to outliers in real-world data.
method COOT infers alignment between features and samples, unbalanced COOT adds robustness.
result Unbalanced COOT is robust to noise in real-world datasets.
Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.
problem Optimal transport with relaxed marginal conditions.
method Reformulate UOT as non-negative penalized linear regression, propose multiplicative updates.
result Efficient algorithms for UOT with quadratic penalties, continuity of solutions.
Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT…
A new method reduces the computational cost of Sinkhorn algorithm for OT and UOT problems.
problem High computational complexity of Sinkhorn algorithm for OT and UOT problems.
method Importance sparsification method called Spar-Sink to efficiently approximate entropy-regularized OT and UOT solutions.
result The method reduces computational cost from O ( n 2 ) O(n^2) O ( n 2 ) to O ~ ( n ) \widetilde{O}(n) O ( n ) , and is consistent under mild regularity conditions. We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most n n n components. We show that the complexity of the Sinkhorn algorithm for finding an ε \varepsilon ε -appr…
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.
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.
New method for comparing different mass measures on tree structures using entropy partial transport.
problem Comparing nonnegative measures with different masses on tree structures.
method Entropy Partial Transport (EPT) on extended trees, regularized for fast computation and negative definiteness.
result First closed-form solution for unbalanced OT on tree structures.
New scalable methods for unbalanced optimal transport improve efficiency and applicability.
problem Scalable algorithms for unbalanced optimal transport remain underexplored.
method Analysis of semi-dual formulation and adaptive gradient methods.
result SGD methods achieve a convergence rate of O(n/εT) for large-scale applications.
Comparing data defined over space and time is notoriously hard, because it involves quantifying both spatial and temporal variability, while at the same time taking into account the chronological structure of data. Dynamic Time Warping (DTW) computes an optimal alignment between time series in agreement with the chrono…
Novel methods robustify Gromov-Wasserstein distance for cross-domain alignment.
problem Robustifying Gromov-Wasserstein distance for cross-domain alignment.
method Three novel techniques derived from robust statistics to improve GW and its variants.
result Empirical validation shows superior resilience to contamination.
A new method for transporting unbalanced measures on graphs efficiently.
problem Optimal transport for measures with unequal total masses on graph metric spaces.
method Developed a novel variant of entropy partial transport (Orlicz-EPT) with Orlicz geometric structure, leading to Orlicz-Sobolev transport (OST).
result OST can be efficiently computed by solving a univariate optimization problem, significantly faster than Orlicz-EPT.
Optimal transport simplifies machine learning by comparing probability measures.
problem Comparing and manipulating probability distributions in machine learning.
method Uses optimal transport to compare and manipulate probability distributions, combining statistical and geometric perspectives.
result Optimal transport provides a unified framework for various machine learning tasks.
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote models using a small subset of regressors. To increase statistical power, the so-c…
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.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
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.
We propose Unbalanced GANs, which pre-trains the generator of the generative adversarial network (GAN) using variational autoencoder (VAE). We guarantee the stable training of the generator by preventing the faster convergence of the discriminator at early epochs. Furthermore, we balance between the generator and the d…
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.
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- …
New formula for instantaneous frequency in unbalanced systems.
problem Estimating frequency in unbalanced electrical systems.
method Utilizes affine differential geometry to link frequency and voltage derivatives.
result Proposes a new formula for instantaneous frequency estimation.
New method clusters strong and weak views effectively, improving performance by up to 40%.
problem Clustering incomplete multi-view data with unbalanced incompleteness.
method View evolution scheme and weighted multi-view subspace clustering.
result Improves clustering performance by up to 40% on three metrics.
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 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.
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.
Training models on highly unbalanced data is admitted to be a challenging task for machine learning algorithms. Current studies on deep learning mainly focus on data sets with balanced class labels or unbalanced data, but with massive amount of samples available, like in speech recognition. However, the capacities of d…
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.
Paper addresses unbalanced data in common shock models for loss reserving.
problem Complications in capturing structural dependence with unbalanced data.
method Introduces a common shock Tweedie approach for unbalanced data.
result Better balance of common shock proportions and parsimonious solution.
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.
Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better differentiation using the Sinkhorn algorithm, as well as better sample complexity bounds …
A simple model for unbalanced optimal transport captures key features.
problem Capturing the main features of unbalanced optimal transport.
method Introducing a metric on the conical extension of diffeomorphisms and studying its properties.
result Total mass evolves with constant acceleration along geodesics.
Unbalanced minibatch Optimal Transport improves domain adaptation performance.
problem Optimal transport distances are computationally expensive for large datasets.
method Use unbalanced minibatch Optimal Transport to estimate distances over subsets of data.
result Unbalanced Optimal Transport leads to better domain adaptation results.
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.
The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.
problem Understanding the balance of conflict graphs in Petersen family graphs.
method Analyzing maximally planar subgraphs and their conflict graphs.
result All but three strong conflict graphs from Petersen Family Graphs are unbalanced.
Estimates mean and covariance for large, unbalanced stock returns panels.
problem Estimating mean and covariance in large, unbalanced panel data.
method Nonparametric, kernel-based joint estimator for conditional mean and covariance matrices.
result The idiosyncratic risk explains more than 75% of cross-sectional variance.
Proposes a method to stabilize treatment effect estimation with unbalanced data.
problem Unbalanced treatment assignment leading to unstable propensity score estimations.
method Undersamples data for propensity score modeling and calibrates scores to match original distribution.
result The estimator retains asymptotic properties of the DML estimator and improves finite sample performance.