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Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain.…
Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised…
Predictive performance of machine learning models trained with empirical risk minimization (ERM) can degrade considerably under distribution shifts. The presence of spurious correlations in training datasets leads ERM-trained models to…
Motivated by gene set enrichment analysis, we investigate the problem of combined hypothesis testing on a graph. We introduce a general framework to effectively use the structural information of the underlying graph when testing…
Minimum spanning trees (MSTs) are used in a variety of fields, from computer science to geography. Infectious disease researchers have used them to infer the transmission pathway of certain pathogens. However, these are often the MSTs of…
We study the problem of testing triangle freeness in the general graph model. This problem was first studied in the general graph model by Alon et al. (SIAM J. Discret. Math. 2008) who provided both lower bounds and upper bounds that depend…
Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely…
Graph Neural Networks (GNNs) often perform better for high-degree nodes than low-degree nodes on node classification tasks. This degree bias can reinforce social marginalization by, e.g., privileging celebrities and other high-degree actors…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model…
The present study was concerned with network failure problems for simple connected undirected graphs. A connected graph becomes unconnected through edge failure, under the assumptions that only edges can fail and each edge has an identical…
Graph Neural Network (GNN) is an emerging technique for graph-based learning tasks such as node classification. In this work, we reveal the vulnerability of GNN to the imbalance of node labels. Traditional solutions for imbalanced…
Given a network represented by a graph $G=(V,E)$, we consider a dynamical process of influence diffusion in $G$ that evolves as follows: Initially only the nodes of a given $S\subseteq V$ are influenced; subsequently, at each round, the set…
Graph Neural Networks (GNNs) have made tremendous progress in the graph classification task. However, a performance gap between the training set and the test set has often been noticed. To bridge such gap, in this work we introduce the…
Graph Neural Networks (GNNs) are the predominant technique for learning over graphs. However, there is relatively little understanding of why GNNs are successful in practice and whether they are necessary for good performance. Here, we show…
In this article, we extend a statistical test of graph clusterability, the $\delta$ test, to directed graphs with no self loops. The $\delta$ test, originally designed for undirected graphs, is based on the premise that graphs with a…
We propose a combinatorial optimisation model called Limited Query Graph Connectivity Test. We consider a graph whose edges have two possible states (On/Off). The edges' states are hidden initially. We could query an edge to reveal its…