Fast and reliable inference algorithm for hierarchical stochastic block models

Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity behaviour, with nodes behaving similarly belonging to the same community. In this context, mixture modelling is pursued through stochastic blockmodelling. We consider stochastic blockmodels and some of their variants and extensions from a mixture mo...

An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel (SBM) with block parameters integrated out. The resulting marginal distribution defines a posterior over the number of clusters and cluster memberships. Sampling from this posterior is simpler than from the original SBM as transdimensional...

Community detection for large networks is a challenging task due to the high computational cost as well as the heterogeneous community structure. Stochastic block model (SBM) is a popular model to analyze community structure where nodes belonging to the same communities are connected with equal probability. Modularity optimization methods provide a fast and effective way for community detection under SBM with assortative community structure, where nodes within communities are...

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e. continuous or discrete, signed or unsig...

It has been shown that community detection algorithms work better for clustering tasks than other, more popular methods, such as k-means. In fact, network analysis based methods often outperform more widely used methods and do not suffer from some of the drawbacks we notice elsewhere e.g. the number of clusters k usually has to be known in advance. However, stochastic block models which are known to perform well for community detection, have not yet been tested for this task....

The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network reconstruction approaches based on Bayesian inference. These approaches, however, rely on assumptions of uniform error rates and on direct estimations of the existence of each edge via repeated measurements, something that is currently unavai...

A principled approach to characterize the hidden structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empiri...

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. One prominent work that overcomes this computational challenge is Amini et al.(2013), which proposed a fast pseudo-likelihood approach for fitting stochastic block models to large sparse networks. However, this approach does not have converge...

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a ...

Analysis of the topology of a graph, regular or bipartite one, can be done by clustering for regular ones or co-clustering for bipartite ones. The Stochastic Block Model and the Latent Block Model are two models, which are very similar for respectively regular and bipartite graphs, based on probabilistic models. Initially developed for binary graphs, these models have been extended to valued networks with optional covariates on the edges. This paper present a implementation o...