--- _id: '2009' abstract: - lang: eng 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. article_processing_charge: No author: - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Aleksandra full_name: Slavkovic, Aleksandra last_name: Slavkovic - first_name: Stephen full_name: Fienberg, Stephen last_name: Fienberg citation: 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 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 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. 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. 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. 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. short: C. Uhler, A. Slavkovic, S. Fienberg, Journal of Privacy and Confidentiality 5 (2013) 137–166. date_created: 2018-12-11T11:55:11Z date_published: 2013-08-01T00:00:00Z date_updated: 2021-01-12T06:54:41Z day: '01' department: - _id: CaUh doi: 10.29012/jpc.v5i1.629 intvolume: ' 5' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://repository.cmu.edu/jpc/vol5/iss1/6 month: '08' oa: 1 oa_version: Published Version page: 137 - 166 publication: 'Journal of Privacy and Confidentiality ' publication_status: published publisher: Carnegie Mellon University publist_id: '5067' quality_controlled: '1' status: public title: Privacy-preserving data sharing for genome-wide association studies type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 5 year: '2013' ... --- _id: '2010' abstract: - lang: eng 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. arxiv: 1 author: - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Garvesh full_name: Raskutti, Garvesh last_name: Raskutti - first_name: Peter full_name: Bühlmann, Peter last_name: Bühlmann - first_name: Bin full_name: Yu, Bin last_name: Yu citation: 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 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. 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. 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. 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. short: C. Uhler, G. Raskutti, P. Bühlmann, B. Yu, The Annals of Statistics 41 (2013) 436–463. date_created: 2018-12-11T11:55:11Z date_published: 2013-04-01T00:00:00Z date_updated: 2021-01-12T06:54:42Z day: '01' department: - _id: CaUh doi: 10.1214/12-AOS1080 external_id: arxiv: - '1207.0547' intvolume: ' 41' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: www.doi.org/10.1214/12-AOS1080 month: '04' oa: 1 oa_version: Published Version page: 436 - 463 publication: The Annals of Statistics publication_status: published publisher: Institute of Mathematical Statistics publist_id: '5066' quality_controlled: '1' scopus_import: 1 status: public title: Geometry of the faithfulness assumption in causal inference type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 41 year: '2013' ... --- _id: '2280' 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. arxiv: 1 author: - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Stephen full_name: Wright, Stephen last_name: Wright citation: 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 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. 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. ista: Uhler C, Wright S. 2013. Packing ellipsoids with overlap. SIAM Review. 55(4), 671–706. 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. short: C. Uhler, S. Wright, SIAM Review 55 (2013) 671–706. date_created: 2018-12-11T11:56:44Z date_published: 2013-11-07T00:00:00Z date_updated: 2021-01-12T06:56:30Z day: '07' department: - _id: CaUh doi: 10.1137/120872309 external_id: arxiv: - '1204.0235' intvolume: ' 55' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1204.0235 month: '11' oa: 1 oa_version: Preprint page: 671 - 706 publication: SIAM Review publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '4655' quality_controlled: '1' scopus_import: 1 status: public title: Packing ellipsoids with overlap type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2013' ... --- _id: '2959' abstract: - lang: eng 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. 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" author: - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 citation: 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 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 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. 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. 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. date_created: 2018-12-11T12:00:33Z date_published: 2012-02-01T00:00:00Z date_updated: 2021-01-12T07:40:04Z day: '01' department: - _id: CaUh doi: 10.1214/11-AOS957 intvolume: ' 40' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1012.2643 month: '02' oa: 1 oa_version: Preprint page: 238 - 261 publication: Annals of Statistics publication_status: published publisher: Institute of Mathematical Statistics publist_id: '3767' quality_controlled: '1' scopus_import: 1 status: public title: Geometry of maximum likelihood estimation in Gaussian graphical models type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 40 year: '2012' ...