Note on the computational complexity of Gromov-Wasserstein distance.
problem Computational difficulty of Gromov-Wasserstein distance.
method Analysis of the optimization problem structure and providing explicit examples.
result Gromov-Wasserstein distance optimization problem is non-convex quadratic.
A method for learning embeddings from multi-view data using Gromov-Wasserstein.
problem Challenges in learning low-dimensional representations from multi-view relational data with differing geometries.
method Bary-GWMDS and Mean-GWMDS-C, Gromov-Wasserstein-based methods operating on distance matrices.
result Stable and geometrically meaningful embeddings learned from synthetic and real-world datasets.
Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.
problem Graph distances overlook edge attributes, limiting their effectiveness.
method Introduced Fused Gromov-Wasserstein distance for graph comparison with edge features. Proposed algorithms for distance and barycenter computation.
result Empirically validated the effectiveness of the novel distance in graph learning tasks.
New Gromov-Wasserstein metric controls rigidity and incorporates prior knowledge.
problem Inflexible Gromov-Wasserstein distance and lack of feature alignment.
method Augmented Gromov-Wasserstein distance with feature alignments and prior knowledge.
result Improved performance in single-cell multi-omic alignment and transfer learning.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
A new sliced IGW distance for Gromov-Wasserstein alignment.
problem Scalability issues in Gromov-Wasserstein alignment for high-dimensional problems.
method Proposed a sliced IGW distance with rotational invariance.
result Natural rotational invariance of the sliced IGW distance.
A new conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances.
problem Lack of principled uncertainty quantification for graph-valued supervised prediction.
method Proposes a conformal prediction framework using Z-Gromov-Wasserstein distances for graph-valued outputs.
result Provides distribution-free coverage guarantees for graph-valued outputs.
Method learns graphons from graphs via Gromov-Wasserstein barycenters.
problem Learning nonparametric graph models from finite graphs.
method Approximate graphons with step functions, use Gromov-Wasserstein distance, learn barycenters.
result Proposed method outperforms state-of-the-art on synthetic and real-world data.
Develops a private synthetic graph generator using Gromov-Wasserstein distance.
problem Creating private synthetic networks for complex data.
method Random connection model, fused Gromov-Wasserstein distance, differential privacy.
result Effective algorithm for generating private synthetic graphs with theoretical guarantees.
Paper introduces new Gromov-type distances for comparing Gaussian mixture models.
problem Comparing distributions across different metric spaces using Gromov-Wasserstein distances.
method Incorporates invariance properties into MW2, introducing MGW2 and EW2.
result MGW2 and EW2 are efficient for estimating distances between GMMs in practical applications.
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
problem Matching objects between incomparable spaces using the Gromov-Wasserstein distance.
method Semi-definite programming (SDP) relaxation of the GW distance.
result The SDP relaxation provides globally optimal solutions for the GW distance in some instances.
A new method efficiently approximates Gromov-Wasserstein distance.
problem High computational complexity of Gromov-Wasserstein distance.
method Importance sparsification method to construct a sparse coupling matrix.
result Efficient approximation of GW distance with reduced complexity.
Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects but treat them in…
Implementing k-NN classification using Gromov--Wasserstein distances
problem Comparing metric measure spaces
method Gromov--Wasserstein and fused Gromov--Wasserstein distances
result Universal consistency of k-NN classifiers GWIL uses Gromov-Wasserstein distance to align expert and imitation agent states.
problem Cross-domain imitation learning challenges due to different system dimensions and stationary distributions.
method Gromov-Wasserstein Imitation Learning (GWIL) using Gromov-Wasserstein distance.
result GWIL effectively aligns expert and imitation agent states in various continuous control domains.
Robust GW distance improves graph data alignment.
problem Outliers in GW distance lead to inaccurate comparisons.
method Optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set.
result RGW reduces inaccuracies in graph data alignment.
We introduce a new framework for comparing parametric network families.
problem Comparing and analyzing data modeled as parameterized families of networks.
method A Gromov-Wasserstein variant of optimal transport for defining distances.
result Established foundational properties and theoretical approximation guarantees for the new distances.
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance requires solving a complex non convex quadratic program which is most of the time very…
Robustly aligns datasets with partial GW distance to handle contamination.
problem Aligning contaminated datasets using Gromov-Wasserstein distances.
method Proposes a partial GW distance estimator to minimize distortion from outliers.
result The partial GW distance estimator is minimax optimal and near-optimal in finite samples.
Extends subspace detour method to Gromov-Wasserstein problem.
problem Matching shapes using Gromov-Wasserstein distance.
method Project measures onto a subspace, then compute optimal transport plan.
result Connections with Knothe-Rosenblatt rearrangement.
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 novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node …
GWIB improves counterfactual regression by balancing latent distributions and reducing selection bias.
problem Selection bias between control and treatment groups negatively impacts counterfactual regression performance.
method GWIB uses Gromov-Wasserstein information bottleneck to maximize mutual information between covariates and outcomes while penalizing kernelized mutual information between latent representations and covariates.
result GWIB consistently outperforms state-of-the-art CFR methods in ITE estimation tasks.
This study improves graph coarsening methods by preserving graph spectrum and distances.
problem Solving large-scale graph problems by working on a smaller graph.
method Developed a geometric approach using Gromov--Wasserstein distance to minimize the difference between graph distances and their coarsened versions.
result Minimizing the difference between graph distances and their coarsened versions can be achieved using the weighted kernel K-means method. Proposes an efficient lower bound for Gromov-Wasserstein discrepancy.
problem Comparing structured data from different metric-measure spaces.
method Orthogonal Gromov-Wasserstein (OGW) discrepancy with efficient closed-form lower bound.
result Efficient and tight lower bounds for Gromov-Wasserstein discrepancy.
New formulations for comparing metric measure spaces with arbitrary positive measures.
problem Comparing metric measure spaces with arbitrary positive measures.
method Two novel formulations: a divergence and a conic lifting approach.
result Efficiently solvable formulations for comparing metric spaces with arbitrary positive measures.
This paper introduces a new formulation of the Conic Gromov-Wasserstein distance for comparing complex network structures.
problem Comparing measures of unequal mass and complex network structures.
method Novel semi-coupling formulation and extension to hypernetworks.
result Establishes fundamental properties and robustness of CGW metric.
The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.
problem Properties of Gromov-Wasserstein optimal transport plans.
method Exploration of sparsity, permutation support, and cyclical monotonicity properties.
result GW optimal plans can be sparse and permutation-supported under certain conditions.
A new slicing method reduces computational cost for cross-domain alignment.
problem High computational cost in solving Gromov-Wasserstein distance.
method Relation-Aware Projecting Direction (RAPD) and Relation-Aware Slicing Distribution (RASD).
result RASGW distance reduces computational cost and improves alignment accuracy.
The paper introduces optimal transport kernels for comparing cell complexes.
problem Lack of machine learning methods for CW complexes.
method Derives explicit expression for Wasserstein distance, extends Fused Gromov-Wasserstein, introduces novel kernels.
result Introduced novel kernels for comparing probability measures on CW complexes.
New method improves robust point matching under probabilistic settings.
problem Insufficient theoretical understanding of existing point matching methods.
method Distance profiles and modified matching procedure.
result Improved robustness under probabilistic settings.
Proposes a new metric for comparing shapes in different spaces.
problem Comparing shapes in different metric spaces with unequal mass.
method Developed a Partial Gromov-Wasserstein (PGW) metric and algorithms to solve it.
result PGW is a well-defined metric between metric measure spaces.
Proposes Gromov-Wasserstein methods for multi-view embedding.
problem Integrating multiple representations of the same samples in heterogeneous geometries.
method Gromov-Wasserstein optimal transport for multi-view embedding.
result Preserves intrinsic relational structure across views effectively.
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of …
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order n−2/(d+5). Improved spectral clustering via Gromov-Wasserstein Learning.
problem Optimizing graph partitioning performance.
method Bridge spectral clustering and GWL, using heat kernel for stable node correspondences.
result Improved graph partitioning results without compromising theoretical guarantees.
Adaptive orthogonalization of data for clustering and visualization.
problem Clustering and visualization of data with high specificity.
method Adaptive orthogonalization process using Gromov-Wasserstein feedback.
result Method refines orthogonality of data to achieve high specificity clustering.
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.
We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure their dissimilarity, which considers both the Wasserstein discrepancy based on the…
This thesis tackles Optimal Transport on incomparable spaces, proposing new tools and properties.
problem How to apply Optimal Transport between graphs and structured data in different metric spaces?
method Study of Gromov-Wasserstein distance and development of new Optimal Transport tools.
result Mathematical properties and algorithmic solutions for transport problems on incomparable spaces.
Faster GW alignment for incomparable point clouds via low-rank couplings.
problem Aligning points across incomparable point clouds.
method Low-rank couplings and costs to solve Gromov-Wasserstein framework in linear time.
result Linear-time computation of Gromov-Wasserstein distances.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we consider a method allowing to embed the metric measure spaces in a common Euclidean spa…
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with th…
This work explores gradient flows and Riemannian structure in Gromov-Wasserstein geometry for data with global structure.
problem Suitable geometry for tasks requiring preservation of global data structure.
method Study of gradient flows and Riemannian structure in Gromov-Wasserstein geometry for distributions on \(\mathbb{R}^d\).
result Established a Benamou-Brenier-like formula for IGW and derived the IGW gradient.
Unified framework for DR and clustering using Gromov-Wasserstein.
problem Capturing structure in high-dimensional datasets.
method Distributional reduction framework using Gromov-Wasserstein.
result Unified approach recovers DR and clustering as special cases.
New bounds show empirical EOT adapts to simpler measure.
problem Statistical performance of empirical EOT estimators.
method Novel statistical bounds, empirical process theory, dual formulation.
result Empirical EOT and its unregularized version follow lower complexity adaptation.