{"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/concentration-of-multilinear-functions-of-the","title":"Concentration of Multilinear Functions of the Ising Model with Applications to Network Data","arxiv_id":"1710.04170","date":"2017-10-11","proceeding":"NeurIPS 2017 12","authors":["Constantinos Daskalakis","Nishanth Dikkala","Gautam Kamath"],"abstract":"We prove near-tight concentration of measure for polynomial functions of the\nIsing model under high temperature. For any degree $d$, we show that a\ndegree-$d$ polynomial of a $n$-spin Ising model exhibits exponential tails that\nscale as $\\exp(-r^{2/d})$ at radius $r=\\tilde{\\Omega}_d(n^{d/2})$. Our\nconcentration radius is optimal up to logarithmic factors for constant $d$,\nimproving known results by polynomial factors in the number of spins. We\ndemonstrate the efficacy of polynomial functions as statistics for testing the\nstrength of interactions in social networks in both synthetic and real world\ndata.","url_abs":"http://arxiv.org/abs/1710.04170v1","url_pdf":"http://arxiv.org/pdf/1710.04170v1.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":"concentration-of-multilinear-functions-of-the","repo_url":"https://github.com/hoonose/multilinear-ising","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1710.04170","atlas_url":"https://app.syntology.ai/?focus=1710.04170","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}