Bayesian Stochastic Blockmodeling

Peixoto, Tiago P.

doi:10.1002/9781119483298.ch11

Cited by 137 publications

(156 citation statements)

References 115 publications

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“…Two of the recent developments are worth singling out. The first is the nested microcanonical SBM (Peixoto, 2017a), which establishes the MDL (Peixoto, 2013) and its equivalence with the usual Bayesian inference approach, incorporates an efficient MCMC algorithm (Peixoto, 2014a) and a hierarchical structure (Peixoto, 2014b) to model K and circumvent the issue with potential underfitting due to the maximum K detectable in an SBM (Peixoto, 2013). One possible direction is to apply these methods and techniques to hypergraphs as well, as they are still a growing field to our knowledge.…”

Section: Discussionmentioning

confidence: 99%

“…(We refrain from calling it the marginal likelihood, which we refer to the likelihood with Z also integrated out.) Furthermore, this π(Y|Z, λ) can be split into the product of the two underbraced terms, which is the joint likelihood of a microcanonical model (Peixoto, 2017a). It is termed "microcanonical" because of the hard constraints imposed, as Y and Z together fix the value of E, and therefore π(Y|Z, λ) = π(Y, E|Z, λ) = π(Y|E, Z, λ) × π(E|Z, λ).…”

Section: Microcanonical Sbmmentioning

confidence: 99%

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A review of stochastic block models and extensions for graph clustering

Lee¹,

Wilkinson²

2019

Appl Netw Sci

158

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There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the type of the graph, the clustering approach, the inference approach, and whether the number of groups is selected or estimated. We also review models that combine block modelling with topic modelling and/or longitudinal modelling, regarding how these models deal with multiple types of data. How different approaches cope with various issues will be summarised and compared, to facilitate the demand of practitioners for a concise overview of the current status of these areas of literature.

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Section: Discussionmentioning

confidence: 99%

Section: Microcanonical Sbmmentioning

confidence: 99%

A review of stochastic block models and extensions for graph clustering

Lee¹,

Wilkinson²

2019

Appl Netw Sci

158

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“…Another drawback of this approach is that the stochastic block model requires the selection of the number of communities, because selecting a large number of blocks always leads to a high likelihood of generating the observed network. Therefore, recent works [23,24,26] adopt Bayes model selection to find the appropriate number of communities in a network. According to Occam's Razor, this approach also minimizes the description length (MDL) of the block model [25,26] so that community detection algorithm finds the most suitable number of communities.…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively, according to the Occam's Razor, the model inference process can take into account the complexity of the model, which can be measured by the model description length [25]. Other work [26] also uses the Bayesian model selection to determine the number of the communities in a network.…”

Section: Model Inferencementioning

confidence: 99%

On community structure in complex networks: challenges and opportunities

et al. 2019

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Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of a large interdisciplinary community of scientists working on this subject over the past few decades to characterize, model, and analyze communities, more investigations are needed in order to better understand the impact of their structure and dynamics on networked systems. Here, in the first section, we review the work on generative models of communities and their role in developing strong foundation for community detection algorithms. We discuss modularity and algorithms based on modularity maximization. Then we follow with an overview of the Stochastic Block Model and its different variants as well as inference of communities structures from the model. The following section focuses on time evolving networks, where existing nodes and links can disappear, and in parallel new nodes and links may be introduced. The extraction of communities under such circumstances poses an interesting and non-trivial problem that has gained considerable interest over the last decade. We briefly discuss considerable advances made in this field recently. In the last section, we discuss immunization strategies essential for targeting the influential spreaders of epidemics in modular networks. Their main goal is to select and immunize a small proportion of individuals from the whole network to control the diffusion process. Various strategies have emerged over the years suggesting different ways to immunize nodes in networks with overlapping and non-overlapping community structure. We first discuss stochastic strategies that require little or no information about the network topology at the expense of their performance. Then, we introduce deterministic strategies that have proven to be very efficient in controlling the epidemic outbreaks, but require complete knowledge of the network.

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“…Community detection 132 We combined a stochastic block model (SBM) [7] and a consensus clustering approach 133 to uncover the mesoscopic block structure of the correlation networks. In the 134 microcanonical formulation of the SBM that we used, one minimizes the description 135 length of the network [8], such that one partitions the nodes in the network G into B by a partition b is given by the following Bayesian posterior probability:…”

mentioning

confidence: 99%

Immune state networks of wild and laboratory mice

Reis

Masuda

Viney³

2019

Preprint

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The mammalian immune system protects individuals from infection and disease. It is a complex system of interacting cells and molecules and extensive work, principally with laboratory mice, has investigated its function. Wild and laboratory animals lead very different lives, and this is reflected in there being substantial immunological differences between them. Here we use network analyses to study a unique data set of 120 immune measures of wild and laboratory mice, where immune measures define nodes and correlations of immune measures across individual mice define edges between immune measures. To date, there has only been very limited network analyses of the immune system, which is surprising because such analyses may be important to better understand its organisation and functionality. We found that the immunological networks of wild and laboratory mice were similar in some aspects of their mesoscale structure, particularly concerning cytokine response communities. However, we also identified notable differences in node membership of network communities between the wild and laboratory networks, pointing to how the same immune system acts and interacts differently in wild and in laboratory mice. These results show the utility of network analysis in understanding immune responses and also the importance of studying wild animals in additional to laboratory animals. Author summaryThe mammalian immune system is a complex system that protects individuals from infection and disease. Most of our understanding of the immune system comes from studies of laboratory animals, particularly mice. However, wild and laboratory animals lead very different lives, potentially leading to substantial immunological differences between them and so possibly limiting the utility of laboratory animals as informative model systems. As a complex interacting set of cells and molecules, the immune system is a biological network. Therefore, we used network analyses to study the immune system, specifically a unique data set of immune measures of wild and laboratory mice, where 120 different immune measures define nodes of the network. We found that the networks of wild and laboratory mice were similar in some aspects of their grouping structure, particularly concerning communities of nodes of cytokine responses. However, we also identified notable differences in node membership of communities between the wild and laboratory networks, pointing to how the same immune system behaves differently in wild and in laboratory mice. These results show the utility of network May 9, 2019 1/19 analysis in understanding immune responses and also the importance of studying wild animals in addition to laboratory animals.1 The vertebrate immune system defends animals against infection and disease. 2Understanding how the immune system functions has been a long-standing area of 3 study, not only to understand the basic biology of this important system, but also to be 4 able to manipulate it for therapeutic benefit. Almost all that we know about the 5 mammalian...

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Bayesian Stochastic Blockmodeling

Cited by 137 publications

References 115 publications

A review of stochastic block models and extensions for graph clustering

A review of stochastic block models and extensions for graph clustering

On community structure in complex networks: challenges and opportunities

Immune state networks of wild and laboratory mice

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