[{"scopus_import":1,"main_file_link":[{"url":"www.doi.org/10.1214/12-AOS1080","open_access":"1"}],"month":"04","intvolume":" 41","abstract":[{"text":"Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for the PC-algorithm and potentially also for other algorithms based on partial correlation testing in the Gaussian case.","lang":"eng"}],"oa_version":"Published Version","issue":"2","volume":41,"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"2010","department":[{"_id":"CaUh"}],"date_updated":"2021-01-12T06:54:42Z","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"page":"436 - 463","doi":"10.1214/12-AOS1080","date_published":"2013-04-01T00:00:00Z","date_created":"2018-12-11T11:55:11Z","year":"2013","day":"01","publication":"The Annals of Statistics","publist_id":"5066","author":[{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","first_name":"Caroline","full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216","last_name":"Uhler"},{"first_name":"Garvesh","last_name":"Raskutti","full_name":"Raskutti, Garvesh"},{"first_name":"Peter","last_name":"Bühlmann","full_name":"Bühlmann, Peter"},{"last_name":"Yu","full_name":"Yu, Bin","first_name":"Bin"}],"external_id":{"arxiv":["1207.0547"]},"title":"Geometry of the faithfulness assumption in causal inference","citation":{"mla":"Uhler, Caroline, et al. “Geometry of the Faithfulness Assumption in Causal Inference.” The Annals of Statistics, vol. 41, no. 2, Institute of Mathematical Statistics, 2013, pp. 436–63, doi:10.1214/12-AOS1080.","ama":"Uhler C, Raskutti G, Bühlmann P, Yu B. Geometry of the faithfulness assumption in causal inference. The Annals of Statistics. 2013;41(2):436-463. doi:10.1214/12-AOS1080","apa":"Uhler, C., Raskutti, G., Bühlmann, P., & Yu, B. (2013). Geometry of the faithfulness assumption in causal inference. The Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/12-AOS1080","short":"C. Uhler, G. Raskutti, P. Bühlmann, B. Yu, The Annals of Statistics 41 (2013) 436–463.","ieee":"C. Uhler, G. Raskutti, P. Bühlmann, and B. Yu, “Geometry of the faithfulness assumption in causal inference,” The Annals of Statistics, vol. 41, no. 2. Institute of Mathematical Statistics, pp. 436–463, 2013.","chicago":"Uhler, Caroline, Garvesh Raskutti, Peter Bühlmann, and Bin Yu. “Geometry of the Faithfulness Assumption in Causal Inference.” The Annals of Statistics. Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/12-AOS1080.","ista":"Uhler C, Raskutti G, Bühlmann P, Yu B. 2013. Geometry of the faithfulness assumption in causal inference. The Annals of Statistics. 41(2), 436–463."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"status":"public","type":"journal_article","_id":"2009","department":[{"_id":"CaUh"}],"title":"Privacy-preserving data sharing for genome-wide association studies","article_processing_charge":"No","publist_id":"5067","author":[{"last_name":"Uhler","full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216","first_name":"Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Aleksandra","last_name":"Slavkovic","full_name":"Slavkovic, Aleksandra"},{"full_name":"Fienberg, Stephen","last_name":"Fienberg","first_name":"Stephen"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Uhler, Caroline, et al. “Privacy-Preserving Data Sharing for Genome-Wide Association Studies.” Journal of Privacy and Confidentiality , vol. 5, no. 1, Carnegie Mellon University, 2013, pp. 137–66, doi:10.29012/jpc.v5i1.629.","apa":"Uhler, C., Slavkovic, A., & Fienberg, S. (2013). Privacy-preserving data sharing for genome-wide association studies. Journal of Privacy and Confidentiality . Carnegie Mellon University. https://doi.org/10.29012/jpc.v5i1.629","ama":"Uhler C, Slavkovic A, Fienberg S. Privacy-preserving data sharing for genome-wide association studies. Journal of Privacy and Confidentiality . 2013;5(1):137-166. doi:10.29012/jpc.v5i1.629","short":"C. Uhler, A. Slavkovic, S. Fienberg, Journal of Privacy and Confidentiality 5 (2013) 137–166.","ieee":"C. Uhler, A. Slavkovic, and S. Fienberg, “Privacy-preserving data sharing for genome-wide association studies,” Journal of Privacy and Confidentiality , vol. 5, no. 1. Carnegie Mellon University, pp. 137–166, 2013.","chicago":"Uhler, Caroline, Aleksandra Slavkovic, and Stephen Fienberg. “Privacy-Preserving Data Sharing for Genome-Wide Association Studies.” Journal of Privacy and Confidentiality . Carnegie Mellon University, 2013. https://doi.org/10.29012/jpc.v5i1.629.","ista":"Uhler C, Slavkovic A, Fienberg S. 2013. Privacy-preserving data sharing for genome-wide association studies. Journal of Privacy and Confidentiality . 5(1), 137–166."},"date_updated":"2021-01-12T06:54:41Z","intvolume":" 5","month":"08","main_file_link":[{"url":"http://repository.cmu.edu/jpc/vol5/iss1/6","open_access":"1"}],"oa":1,"quality_controlled":"1","publisher":"Carnegie Mellon University","oa_version":"Published Version","abstract":[{"text":"Traditional statistical methods for confidentiality protection of statistical databases do not scale well to deal with GWAS databases especially in terms of guarantees regarding protection from linkage to external information. The more recent concept of differential privacy, introduced by the cryptographic community, is an approach which provides a rigorous definition of privacy with meaningful privacy guarantees in the presence of arbitrary external information, although the guarantees may come at a serious price in terms of data utility. Building on such notions, we propose new methods to release aggregate GWAS data without compromising an individual’s privacy. We present methods for releasing differentially private minor allele frequencies, chi-square statistics and p-values. We compare these approaches on simulated data and on a GWAS study of canine hair length involving 685 dogs. We also propose a privacy-preserving method for finding genome-wide associations based on a differentially-private approach to penalized logistic regression.","lang":"eng"}],"date_created":"2018-12-11T11:55:11Z","issue":"1","volume":5,"doi":"10.29012/jpc.v5i1.629","date_published":"2013-08-01T00:00:00Z","page":"137 - 166","publication":"Journal of Privacy and Confidentiality ","language":[{"iso":"eng"}],"day":"01","year":"2013","publication_status":"published"},{"date_published":"2013-11-07T00:00:00Z","doi":"10.1137/120872309","date_created":"2018-12-11T11:56:44Z","page":"671 - 706","day":"07","publication":"SIAM Review","year":"2013","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1,"title":"Packing ellipsoids with overlap","author":[{"last_name":"Uhler","full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216","first_name":"Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Wright, Stephen","last_name":"Wright","first_name":"Stephen"}],"publist_id":"4655","external_id":{"arxiv":["1204.0235"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Uhler, Caroline, and Stephen Wright. “Packing Ellipsoids with Overlap.” SIAM Review, vol. 55, no. 4, Society for Industrial and Applied Mathematics , 2013, pp. 671–706, doi:10.1137/120872309.","ama":"Uhler C, Wright S. Packing ellipsoids with overlap. SIAM Review. 2013;55(4):671-706. doi:10.1137/120872309","apa":"Uhler, C., & Wright, S. (2013). Packing ellipsoids with overlap. SIAM Review. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/120872309","ieee":"C. Uhler and S. Wright, “Packing ellipsoids with overlap,” SIAM Review, vol. 55, no. 4. Society for Industrial and Applied Mathematics , pp. 671–706, 2013.","short":"C. Uhler, S. Wright, SIAM Review 55 (2013) 671–706.","chicago":"Uhler, Caroline, and Stephen Wright. “Packing Ellipsoids with Overlap.” SIAM Review. Society for Industrial and Applied Mathematics , 2013. https://doi.org/10.1137/120872309.","ista":"Uhler C, Wright S. 2013. Packing ellipsoids with overlap. SIAM Review. 55(4), 671–706."},"volume":55,"issue":"4","language":[{"iso":"eng"}],"publication_status":"published","month":"11","intvolume":" 55","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1204.0235","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computational experience is described and illustrated. The motivating application-chromosome organization in the human cell nucleus-is discussed briefly, and some illustrative results are presented."}],"department":[{"_id":"CaUh"}],"date_updated":"2021-01-12T06:56:30Z","status":"public","type":"journal_article","_id":"2280"},{"department":[{"_id":"CaUh"}],"date_updated":"2021-01-12T07:40:04Z","type":"journal_article","status":"public","_id":"2959","issue":"1","volume":40,"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1012.2643"}],"scopus_import":1,"intvolume":" 40","month":"02","abstract":[{"text":"We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one, even when the number of observations equals the treewidth.","lang":"eng"}],"oa_version":"Preprint","publist_id":"3767","author":[{"last_name":"Uhler","orcid":"0000-0002-7008-0216","full_name":"Uhler, Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","first_name":"Caroline"}],"title":"Geometry of maximum likelihood estimation in Gaussian graphical models","citation":{"chicago":"Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models.” Annals of Statistics. Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/11-AOS957.","ista":"Uhler C. 2012. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 40(1), 238–261.","mla":"Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models.” Annals of Statistics, vol. 40, no. 1, Institute of Mathematical Statistics, 2012, pp. 238–61, doi:10.1214/11-AOS957.","short":"C. Uhler, Annals of Statistics 40 (2012) 238–261.","ieee":"C. Uhler, “Geometry of maximum likelihood estimation in Gaussian graphical models,” Annals of Statistics, vol. 40, no. 1. Institute of Mathematical Statistics, pp. 238–261, 2012.","apa":"Uhler, C. (2012). Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/11-AOS957","ama":"Uhler C. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 2012;40(1):238-261. doi:10.1214/11-AOS957"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"238 - 261","date_created":"2018-12-11T12:00:33Z","date_published":"2012-02-01T00:00:00Z","doi":"10.1214/11-AOS957","year":"2012","publication":"Annals of Statistics","day":"01","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","acknowledgement":"I wish to thank Bernd Sturmfels for many helpful discus- sions and Steffen Lauritzen for introducing me to the problem of the existence of the MLE in Gaussian graphical models. I would also like to thank two referees who provided helpful comments on the original version of this paper.\r\n"}]