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Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them…

We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number…

Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…

Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…

Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous,…

We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be…

Graph similarity computation (GSC) is to calculate the similarity between one pair of graphs, which is a fundamental problem with fruitful applications in the graph community. In GSC, graph edit distance (GED) and maximum common subgraph…

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…

This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon…

In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…

The rapid growth of graph data creates significant scalability challenges as most graph algorithms scale quadratically with size. To mitigate these issues, Graph Condensation (GC) methods have been proposed to learn a small graph from a…

Autonomous agents rely on sensor data to construct representations of their environments, essential for predicting future events and planning their actions. However, sensor measurements suffer from limited range, occlusions, and sensor…

The success of graph neural networks (GNNs) provokes the question about explainability: ``Which fraction of the input graph is the most determinant of the prediction?'' Particularly, parametric explainers prevail in existing approaches…

Graph similarity learning (GSL), also referred to as graph matching in many scenarios, is a fundamental problem in computer vision, pattern recognition, and graph learning. However, previous GSL methods assume that graphs are homogeneous…

Graph signal processing has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In…