{"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/sampling-and-inference-for-beta-neutral-to","title":"Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks","arxiv_id":"1807.03113","date":"2018-07-09","proceeding":null,"authors":["Benjamin Bloem-Reddy","Adam Foster","Emile Mathieu","Yee Whye Teh"],"abstract":"Empirical evidence suggests that heavy-tailed degree distributions occurring\nin many real networks are well-approximated by power laws with exponents $\\eta$\nthat may take values either less than and greater than two. Models based on\nvarious forms of exchangeability are able to capture power laws with $\\eta <\n2$, and admit tractable inference algorithms; we draw on previous results to\nshow that $\\eta > 2$ cannot be generated by the forms of exchangeability used\nin existing random graph models. Preferential attachment models generate power\nlaw exponents greater than two, but have been of limited use as statistical\nmodels due to the inherent difficulty of performing inference in\nnon-exchangeable models. Motivated by this gap, we design and implement\ninference algorithms for a recently proposed class of models that generates\n$\\eta$ of all possible values. We show that although they are not exchangeable,\nthese models have probabilistic structure amenable to inference. Our methods\nmake a large class of previously intractable models useful for statistical\ninference.","url_abs":"http://arxiv.org/abs/1807.03113v1","url_pdf":"http://arxiv.org/pdf/1807.03113v1.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":"sampling-and-inference-for-beta-neutral-to","repo_url":"https://github.com/emilemathieu/NTL.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}