Related papers: The Hierarchy of Block Models
Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into $\mathbb{R}^{d}$ using spectral methods. The resulting point cloud concentrates…
Many kinds of data can be represented as a network or graph. It is crucial to infer the latent structure underlying such a network and to predict unobserved links in the network. Mixed Membership Stochastic Blockmodel (MMSB) is a promising…
Significant progress has been made recently on theoretical analysis of estimators for the stochastic block model (SBM). In this paper, we consider the multi-graph SBM, which serves as a foundation for many application settings including…
Network neutrality (NN) is a principle of equal treatment of data in network infrastructures with fairness and universality being the primary outcomes of the NN management practice. For networks, the accomplishment of NN management practice…
This paper considers the problem of community detection on multiple potentially correlated graphs from an information-theoretical perspective. We first put forth a random graph model, called the multi-view stochastic block model (MVSBM),…
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…
We consider the problem of community detection or clustering in the labeled Stochastic Block Model (LSBM) with a finite number $K$ of clusters of sizes linearly growing with the global population of items $n$. Every pair of items is labeled…
In the node classification task, it is natural to presume that densely connected nodes tend to exhibit similar attributes. Given this, it is crucial to first define what constitutes a dense connection and to develop a reliable mathematical…
In economics and social science, network data are regularly observed, and a thorough understanding of the network community structure facilitates the comprehension of economic patterns and activities. Consider an undirected network with $n$…
Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…
Due to the widespread use of complex machine learning models in real-world applications, it is becoming critical to explain model predictions. However, these models are typically black-box deep neural networks, explained post-hoc via…
Graph embeddings have emerged as a powerful tool for understanding the structure of graphs. Unlike classical spectral methods, recent methods such as DeepWalk, Node2Vec, etc. are based on solving nonlinear optimization problems on the…
Graph Representation Learning (GRL) has become central for characterizing structures of complex networks and performing tasks such as link prediction, node classification, network reconstruction, and community detection. Whereas numerous…
Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such…
Multiple-group data is widely used in genomic studies, finance, and social science. This study investigates a block structure that consists of covariate and response groups. It examines the block-selection problem of high-dimensional models…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an…
The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in recovering communities in the SBM from statistical and computational points of view, there are still…
Community detection is one of the most critical problems in modern network science. Its applications can be found in various fields, from protein modeling to social network analysis. Recently, many papers appeared studying the problem of…
We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood…