{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/nonparametric-bayesian-inference-of-the","title":"Nonparametric Bayesian inference of the microcanonical stochastic block model","arxiv_id":"1610.02703","date":"2016-10-09","proceeding":null,"authors":["Tiago P. Peixoto"],"abstract":"A principled approach to characterize the hidden structure of networks is to\nformulate generative models, and then infer their parameters from data. When\nthe desired structure is composed of modules or \"communities\", a suitable\nchoice for this task is the stochastic block model (SBM), where nodes are\ndivided into groups, and the placement of edges is conditioned on the group\nmemberships. Here, we present a nonparametric Bayesian method to infer the\nmodular structure of empirical networks, including the number of modules and\ntheir hierarchical organization. We focus on a microcanonical variant of the\nSBM, where the structure is imposed via hard constraints, i.e. the generated\nnetworks are not allowed to violate the patterns imposed by the model. We show\nhow this simple model variation allows simultaneously for two important\nimprovements over more traditional inference approaches: 1. Deeper Bayesian\nhierarchies, with noninformative priors replaced by sequences of priors and\nhyperpriors, that not only remove limitations that seriously degrade the\ninference on large networks, but also reveal structures at multiple scales; 2.\nA very efficient inference algorithm that scales well not only for networks\nwith a large number of nodes and edges, but also with an unlimited number of\nmodules. We show also how this approach can be used to sample modular\nhierarchies from the posterior distribution, as well as to perform model\nselection. We discuss and analyze the differences between sampling from the\nposterior and simply finding the single parameter estimate that maximizes it.\nFurthermore, we expose a direct equivalence between our microcanonical approach\nand alternative derivations based on the canonical SBM.","url_abs":"http://arxiv.org/abs/1610.02703v4","url_pdf":"http://arxiv.org/pdf/1610.02703v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"nonparametric-bayesian-inference-of-the","repo_url":"https://git.skewed.de/count0/graph-tool","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"stochastic-block-model","task_name":"Stochastic Block Model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1610.02703","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}