{"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:55:12Z","oa_version":"Submitted Version","oa":1,"scopus_import":1,"publisher":"Springer","status":"public","title":"Hypersurfaces and their singularities in partial correlation testing","quality_controlled":"1","day":"10","type":"journal_article","date_updated":"2021-01-12T06:54:43Z","month":"10","issue":"5","date_published":"2014-10-10T00:00:00Z","publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1209.0285"}],"abstract":[{"text":"An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC algorithm and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow ties, tripartite graphs, and complete graphs.\r\n","lang":"eng"}],"department":[{"_id":"CaUh"}],"volume":14,"publist_id":"5063","intvolume":"        14","year":"2014","acknowledgement":"This work was supported in part by the US National Science Foundation (DMS-0968882) and the Defense Advanced Research Projects Agency (DARPA) Deep Learning program (FA8650-10-C-7020).","publication":"Foundations of Computational Mathematics","author":[{"first_name":"Shaowei","last_name":"Lin","full_name":"Lin, Shaowei"},{"first_name":"Caroline","last_name":"Uhler","full_name":"Uhler, Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216"},{"full_name":"Sturmfels, Bernd","last_name":"Sturmfels","first_name":"Bernd"},{"last_name":"Bühlmann","first_name":"Peter","full_name":"Bühlmann, Peter"}],"page":"1079 - 1116","doi":"10.1007/s10208-014-9205-0","citation":{"mla":"Lin, Shaowei, et al. “Hypersurfaces and Their Singularities in Partial Correlation Testing.” <i>Foundations of Computational Mathematics</i>, vol. 14, no. 5, Springer, 2014, pp. 1079–116, doi:<a href=\"https://doi.org/10.1007/s10208-014-9205-0\">10.1007/s10208-014-9205-0</a>.","ieee":"S. Lin, C. Uhler, B. Sturmfels, and P. Bühlmann, “Hypersurfaces and their singularities in partial correlation testing,” <i>Foundations of Computational Mathematics</i>, vol. 14, no. 5. Springer, pp. 1079–1116, 2014.","ista":"Lin S, Uhler C, Sturmfels B, Bühlmann P. 2014. Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. 14(5), 1079–1116.","chicago":"Lin, Shaowei, Caroline Uhler, Bernd Sturmfels, and Peter Bühlmann. “Hypersurfaces and Their Singularities in Partial Correlation Testing.” <i>Foundations of Computational Mathematics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s10208-014-9205-0\">https://doi.org/10.1007/s10208-014-9205-0</a>.","apa":"Lin, S., Uhler, C., Sturmfels, B., &#38; Bühlmann, P. (2014). Hypersurfaces and their singularities in partial correlation testing. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-014-9205-0\">https://doi.org/10.1007/s10208-014-9205-0</a>","ama":"Lin S, Uhler C, Sturmfels B, Bühlmann P. Hypersurfaces and their singularities in partial correlation testing. <i>Foundations of Computational Mathematics</i>. 2014;14(5):1079-1116. doi:<a href=\"https://doi.org/10.1007/s10208-014-9205-0\">10.1007/s10208-014-9205-0</a>","short":"S. Lin, C. Uhler, B. Sturmfels, P. Bühlmann, Foundations of Computational Mathematics 14 (2014) 1079–1116."},"_id":"2013","language":[{"iso":"eng"}]}