Related papers: Misspecification Tests on Models of Random Graphs
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. This random graph model is well-characterized by its graphon function, and estimation of the graphon…
Many studies have shown that there are regularities in the way human beings make decisions. However, our ability to obtain models that capture such regularities and can accurately predict unobserved decisions is still limited. We tackle…
This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping…
Structured data in the form of networks are increasingly common in a number of fields, including the social sciences, biology, physics, computer science, and many others. A key task in network analysis is community detection, which…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks.…
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…
We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…
Mesoscopic pattern extraction (MPE) is the problem of finding a partition of the nodes of a complex network that maximizes some objective function. Many well-known network inference problems fall in this category, including, for instance,…
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…
Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…
We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd\H{o}s--R\'{e}nyi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic…
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…
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…
A fundamental problem in network data analysis is to test Erd\"{o}s-R\'{e}nyi model $\mathcal{G}\left(n,\frac{a+b}{2n}\right)$ versus a bisection stochastic block model $\mathcal{G}\left(n,\frac{a}{n},\frac{b}{n}\right)$, where $a,b>0$ are…
The Degree Corrected Stochastic Block Model (DCSBM) was introduced by \cite{karrer2011stochastic} as a generalization of the stochastic block model in which vertices of the same community are allowed to have distinct degree distributions.…
Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures. Despite the computational…