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Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In…

In this work, we propose to train a graph neural network via resampling from a graphon estimate obtained from the underlying network data. More specifically, the graphon or the link probability matrix of the underlying network is first…

Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at…

Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the…

Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…

Community detection refers to the problem of clustering the nodes of a network into groups. Existing inferential methods for community structure mainly focus on unweighted (binary) networks. Many real-world networks are nonetheless weighted…

Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of…

Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…

We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…

Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what constitutes a community has remained evasive, community…

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…

Community detection in graphs has been the subject of many algorithms. Recent methods want to optimize a modularity function which shows a maximum of relationships within communities and found a minimum of inter-community relations. these…

The need to produce accurate estimates of vertex degree in a large network, based on observation of a subnetwork, arises in a number of practical settings. We study a formalized version of this problem, wherein the goal is, given a randomly…

It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…

We treat the statistical inference problems in which one needs to detect and estimate simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the…

How to determine the community structure of complex networks is an open question. It is critical to establish the best strategies for community detection in networks of unknown structure. Here, using standard synthetic benchmarks, we show…

Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…

Large networked systems are constantly exposed to local damages and failures that can alter their functionality. The knowledge of the structure of these systems is however often derived through sampling strategies whose effectiveness at…

Graph Neural Networks (GNNs) have achieved tremendous success in a variety of real-world applications by relying on the fixed graph data as input. However, the initial input graph might not be optimal in terms of specific downstream tasks,…