{"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/quantifying-multivariate-redundancy-with","title":"Quantifying multivariate redundancy with maximum entropy decompositions of mutual information","arxiv_id":"1708.03845","date":"2017-08-13","proceeding":null,"authors":["Daniel Chicharro"],"abstract":"Williams and Beer (2010) proposed a nonnegative mutual information\ndecomposition, based on the construction of redundancy lattices, which allows\nseparating the information that a set of variables contains about a target\nvariable into nonnegative components interpretable as the unique information of\nsome variables not provided by others as well as redundant and synergistic\ncomponents. However, the definition of multivariate measures of redundancy that\ncomply with nonnegativity and conform to certain axioms that capture\nconceptually desirable properties of redundancy has proven to be elusive. We\nhere present a procedure to determine nonnegative multivariate redundancy\nmeasures, within the maximum entropy framework. In particular, we generalize\nexisting bivariate maximum entropy measures of redundancy and unique\ninformation, defining measures of the redundant information that a group of\nvariables has about a target, and of the unique redundant information that a\ngroup of variables has about a target that is not redundant with information\nfrom another group. The two key ingredients for this approach are: First, the\nidentification of a type of constraints on entropy maximization that allows\nisolating components of redundancy and unique redundancy by mirroring them to\nsynergy components. Second, the construction of rooted tree-based\ndecompositions of the mutual information, which conform to the axioms of the\nredundancy lattice by the local implementation at each tree node of binary\nunfoldings of the information using hierarchically related maximum entropy\nconstraints. Altogether, the proposed measures quantify the different\nmultivariate redundancy contributions of a nonnegative mutual information\ndecomposition consistent with the redundancy lattice.","url_abs":"http://arxiv.org/abs/1708.03845v2","url_pdf":"http://arxiv.org/pdf/1708.03845v2.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":"quantifying-multivariate-redundancy-with","repo_url":"https://github.com/Abzinger/Chicharro_PID","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"quantifying-multivariate-redundancy-with","repo_url":"https://github.com/Abzinger/MAXENT3D_PID","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"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}