相关论文: Exact recovery and sharp thresholds of Stochastic …

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the…

We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…

We consider the problem associated to recovering the block structure of an Ising model given independent observations on the binary hypercube. This new model, called the Ising blockmodel, is a perturbation of the mean field approximation of…

The Ising antiferromagnet is an important statistical physics model with close connections to the {\sc Max Cut} problem. Combining spatial mixing arguments with the method of moments and the interpolation method, we pinpoint the replica…

The recent years we have seen the rise of graph neural networks for prediction tasks on graphs. One of the dominant architectures is graph attention due to its ability to make predictions using weighted edge features and not only node…

Cancer is a genetic disorder whose clonal evolution can be monitored by tracking noisy genome-wide copy number variants. We introduce the Copy Number Stochastic Block Model (CN-SBM), a probabilistic framework that jointly clusters samples…

We propose a dynamic network sampling scheme to optimize block recovery for stochastic blockmodel (SBM) in the case where it is prohibitively expensive to observe the entire graph. Theoretically, we provide justification of our proposed…

Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies that aim to improve our understanding of functionalities and evolution patterns of networks. To elucidate the role of higher-order…

We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…

Community detection, which aims to cluster $N$ nodes in a given graph into $r$ distinct groups based on the observed undirected edges, is an important problem in network data analysis. In this paper, the popular stochastic block model (SBM)…

A class of models that have been widely used are the exponential random graph (ERG) models, which form a comprehensive family of models that include independent and dyadic edge models, Markov random graphs, and many other graph…

Community detection, discovering the underlying communities within a network from observed connections, is a fundamental problem in network analysis, yet it remains underexplored for signed networks. In signed networks, both edge connection…

A valued stochastic blockmodel (SBM) is a general way to view networked data in which nodes are grouped into blocks and links between them are measured by counts or labels. This family allows for varying dyad sampling schemes, thereby…

Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all…

Signed network structure discovery has received extensive attention and has become a research focus in the field of network science. However, most of the existing studies are focused on the networks with a single structure, e.g., community…

We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on $n$ nodes, having i.i.d. weights $(\phi_u)_{u=1}^n$ (possibly heavy-tailed), partitioned into $q \geq 2$ asymptotically equal-sized clusters. The model…

Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models…