{"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/exact-partial-information-decompositions-for","title":"Exact partial information decompositions for Gaussian systems based on dependency constraints","arxiv_id":"1803.02030","date":"2018-03-06","proceeding":null,"authors":["James W. Kay","Robin A. A. Ince"],"abstract":"The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a\ntheoretical framework to characterize and quantify the structure of\nmultivariate information sharing. A new method (Idep) has recently been\nproposed for computing a two-predictor PID over discrete spaces.\n[arXiv:1709.06653] A lattice of maximum entropy probability models is\nconstructed based on marginal dependency constraints, and the unique\ninformation that a particular predictor has about the target is defined as the\nminimum increase in joint predictor-target mutual information when that\nparticular predictor-target marginal dependency is constrained. Here, we apply\nthe Idep approach to Gaussian systems, for which the marginally constrained\nmaximum entropy models are Gaussian graphical models. Closed form solutions for\nthe Idep PID are derived for both univariate and multivariate Gaussian systems.\nNumerical and graphical illustrations are provided, together with practical and\ntheoretical comparisons of the Idep PID with the minimum mutual information PID\n(Immi). [arXiv:1411.2832] In particular, it is proved that the Immi method\ngenerally produces larger estimates of redundancy and synergy than does the\nIdep method. In discussion of the practical examples, the PIDs are complemented\nby the use of deviance tests for the comparison of Gaussian graphical models.","url_abs":"http://arxiv.org/abs/1803.02030v1","url_pdf":"http://arxiv.org/pdf/1803.02030v1.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":"exact-partial-information-decompositions-for","repo_url":"https://github.com/robince/partial-info-decomp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"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}