{"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/from-distance-correlation-to-multiscale-graph","title":"From Distance Correlation to Multiscale Graph Correlation","arxiv_id":"1710.09768","date":"2017-10-26","proceeding":null,"authors":["Cencheng Shen","Carey E. Priebe","Joshua T. Vogelstein"],"abstract":"Understanding and developing a correlation measure that can detect general\ndependencies is not only imperative to statistics and machine learning, but\nalso crucial to general scientific discovery in the big data age. In this\npaper, we establish a new framework that generalizes distance correlation --- a\ncorrelation measure that was recently proposed and shown to be universally\nconsistent for dependence testing against all joint distributions of finite\nmoments --- to the Multiscale Graph Correlation (MGC). By utilizing the\ncharacteristic functions and incorporating the nearest neighbor machinery, we\nformalize the population version of local distance correlations, define the\noptimal scale in a given dependency, and name the optimal local correlation as\nMGC. The new theoretical framework motivates a theoretically sound Sample MGC\nand allows a number of desirable properties to be proved, including the\nuniversal consistency, convergence and almost unbiasedness of the sample\nversion. The advantages of MGC are illustrated via a comprehensive set of\nsimulations with linear, nonlinear, univariate, multivariate, and noisy\ndependencies, where it loses almost no power in monotone dependencies while\nachieving better performance in general dependencies, compared to distance\ncorrelation and other popular methods.","url_abs":"http://arxiv.org/abs/1710.09768v3","url_pdf":"http://arxiv.org/pdf/1710.09768v3.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":"from-distance-correlation-to-multiscale-graph","repo_url":"https://github.com/neurodata/mgc-matlab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"scientific-discovery","task_name":"scientific discovery"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}