{"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/generalized-root-models-beyond-pairwise","title":"Generalized Root Models: Beyond Pairwise Graphical Models for Univariate Exponential Families","arxiv_id":"1606.00813","date":"2016-06-02","proceeding":null,"authors":["David I. Inouye","Pradeep Ravikumar","Inderjit S. Dhillon"],"abstract":"We present a novel k-way high-dimensional graphical model called the\nGeneralized Root Model (GRM) that explicitly models dependencies between\nvariable sets of size k > 2---where k = 2 is the standard pairwise graphical\nmodel. This model is based on taking the k-th root of the original sufficient\nstatistics of any univariate exponential family with positive sufficient\nstatistics, including the Poisson and exponential distributions. As in the\nrecent work with square root graphical (SQR) models [Inouye et al.\n2016]---which was restricted to pairwise dependencies---we give the conditions\nof the parameters that are needed for normalization using the radial\nconditionals similar to the pairwise case [Inouye et al. 2016]. In particular,\nwe show that the Poisson GRM has no restrictions on the parameters and the\nexponential GRM only has a restriction akin to negative definiteness. We\ndevelop a simple but general learning algorithm based on L1-regularized\nnode-wise regressions. We also present a general way of numerically\napproximating the log partition function and associated derivatives of the GRM\nunivariate node conditionals---in contrast to [Inouye et al. 2016], which only\nprovided algorithm for estimating the exponential SQR. To illustrate GRM, we\nmodel word counts with a Poisson GRM and show the associated k-sized variable\nsets. We finish by discussing methods for reducing the parameter space in\nvarious situations.","url_abs":"http://arxiv.org/abs/1606.00813v1","url_pdf":"http://arxiv.org/pdf/1606.00813v1.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":"generalized-root-models-beyond-pairwise","repo_url":"https://github.com/davidinouye/sqr-graphical-models","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}