Related papers: Distances for Markov Chains, and Their Differentia…

Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…

We propose a new method, dubbed One Class Signed Distance Function (OCSDF), to perform One Class Classification (OCC) by provably learning the Signed Distance Function (SDF) to the boundary of the support of any distribution. The distance…

We establish a bridge between spectral clustering and Gromov-Wasserstein Learning (GWL), a recent optimal transport-based approach to graph partitioning. This connection both explains and improves upon the state-of-the-art performance of…

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…

The application of large language models (LLMs) to graph data has attracted a lot of attention recently. LLMs allow us to use deep contextual embeddings from pretrained models in text-attributed graphs, where shallow embeddings are often…

Graph Neural Networks (GNNs) are known to match the distinguishing power of the 1-Weisfeiler-Lehman (1-WL) test, and the resulting partitions coincide with the unfolding tree equivalence classes of graphs. Preserving this equivalence, GNNs…

With the impressive growth of network models in practically every scientific and technological area, we are often faced with the need to compare graphs, i.e., to quantify their (dis)similarity using appropriate metrics. This is necessary,…

Logistics optimization nowadays is becoming one of the hottest areas in the AI community. In the past year, significant advancements in the domain were achieved by representing the problem in a form of graph. Another promising area of…

Graph Neural Networks (GNNs) are prominent in handling sparse and unstructured data efficiently and effectively. Specifically, GNNs were shown to be highly effective for node classification tasks, where labelled information is available for…

Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…

Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been…

Structured data, such as graphs, is vital in machine learning due to its capacity to capture complex relationships and interactions. In recent years, the Fused Gromov-Wasserstein (FGW) distance has attracted growing interest because it…

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…

This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…

Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi-marginal GW transport. The former can reduce the…

Network topology optimization (NTO) via busbar splitting can mitigate transmission grid congestion and reduce redispatch costs. However, solving this mixed-integer nonlinear problem for large-scale systems in near-real-time is currently…

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and…

We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation…

Graph Neural Networks (GNNs) have recently been utilized to build Collaborative Filtering (CF) models to predict user preferences based on historical user-item interactions. However, there is relatively little understanding of how GNN-based…