Related papers: Optimal transport distances for directed, weighted…
The Gromov-Wasserstein (GW) distance enables comparing metric measure spaces based solely on their internal structure, making it invariant to isomorphic transformations. This property is particularly useful for comparing datasets that…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a…
(Directed) graphs with node attributes are a common type of data in various applications and there is a vast literature on developing metrics and efficient algorithms for comparing them. Recently, in the graph learning and optimization…
The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW…
We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…
Given a graph pair $(G^1, G^2)$, graph edit distance (GED) is defined as the minimum number of edit operations converting $G^1$ to $G^2$. GED is a fundamental operation widely used in many applications, but its exact computation is NP-hard,…
When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
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…
We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide…
Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation -- potentially losing structural or semantic information. We here introduce OT-GNN, a model that computes graph…
Contrastive learning has shown great promise in the field of graph representation learning. By manually constructing positive/negative samples, most graph contrastive learning methods rely on the vector inner product based similarity metric…
Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal…
We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our…
Comparing structured data from possibly different metric-measure spaces is a fundamental task in machine learning, with applications in, e.g., graph classification. The Gromov-Wasserstein (GW) discrepancy formulates a coupling between the…
Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…