{"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/a-low-variance-consistent-test-of-relative","title":"A low variance consistent test of relative dependency","arxiv_id":"1406.3852","date":"2014-06-15","proceeding":null,"authors":["Wacha Bounliphone","Arthur Gretton","Arthur Tenenhaus","Matthew Blaschko"],"abstract":"We describe a novel non-parametric statistical hypothesis test of relative\ndependence between a source variable and two candidate target variables. Such a\ntest enables us to determine whether one source variable is significantly more\ndependent on a first target variable or a second. Dependence is measured via\nthe Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of\nempirical dependence measures (source-target 1, source-target 2). We test\nwhether the first dependence measure is significantly larger than the second.\nModeling the covariance between these HSIC statistics leads to a provably more\npowerful test than the construction of independent HSIC statistics by\nsub-sampling. The resulting test is consistent and unbiased, and (being based\non U-statistics) has favorable convergence properties. The test can be computed\nin quadratic time, matching the computational complexity of standard empirical\nHSIC estimators. The effectiveness of the test is demonstrated on several\nreal-world problems: we identify language groups from a multilingual corpus,\nand we prove that tumor location is more dependent on gene expression than\nchromosomal imbalances. Source code is available for download at\nhttps://github.com/wbounliphone/reldep.","url_abs":"http://arxiv.org/abs/1406.3852v3","url_pdf":"http://arxiv.org/pdf/1406.3852v3.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":"a-low-variance-consistent-test-of-relative","repo_url":"https://github.com/wbounliphone/reldep","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}