[{"department":[{"_id":"CaUh"}],"publisher":"Wiley","publication_status":"published","year":"2015","acknowledgement":"Part of the material presented here was contained in the PhD thesis of the first author to which the second author and Thomas Richardson were advisers. The authors wish to thank him for several comments and suggestions. We also thank the reviewers and the Associate Editor for helpful comments. The proof of Proposition 1 uses the idea of Olga Klimova, to whom the authors are also indebted. The second author was supported in part by Grant K-106154 from the Hungarian National Scientific Research Fund (OTKA).","volume":42,"date_updated":"2021-01-12T06:54:41Z","date_created":"2018-12-11T11:55:11Z","author":[{"full_name":"Klimova, Anna","id":"31934120-F248-11E8-B48F-1D18A9856A87","first_name":"Anna","last_name":"Klimova"},{"full_name":"Rudas, Tamás","first_name":"Tamás","last_name":"Rudas"}],"publist_id":"5068","quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1307.3282"}],"language":[{"iso":"eng"}],"doi":"10.1111/sjos.12139","month":"09","intvolume":" 42","title":"Iterative scaling in curved exponential families","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2008","oa_version":"Preprint","type":"journal_article","issue":"3","abstract":[{"lang":"eng","text":"The paper describes a generalized iterative proportional fitting procedure that can be used for maximum likelihood estimation in a special class of the general log-linear model. The models in this class, called relational, apply to multivariate discrete sample spaces that do not necessarily have a Cartesian product structure and may not contain an overall effect. When applied to the cell probabilities, the models without the overall effect are curved exponential families and the values of the sufficient statistics are reproduced by the MLE only up to a constant of proportionality. The paper shows that Iterative Proportional Fitting, Generalized Iterative Scaling, and Improved Iterative Scaling fail to work for such models. The algorithm proposed here is based on iterated Bregman projections. As a by-product, estimates of the multiplicative parameters are also obtained. An implementation of the algorithm is available as an R-package."}],"page":"832 - 847","citation":{"mla":"Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential Families.” Scandinavian Journal of Statistics, vol. 42, no. 3, Wiley, 2015, pp. 832–47, doi:10.1111/sjos.12139.","short":"A. Klimova, T. Rudas, Scandinavian Journal of Statistics 42 (2015) 832–847.","chicago":"Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential Families.” Scandinavian Journal of Statistics. Wiley, 2015. https://doi.org/10.1111/sjos.12139.","ama":"Klimova A, Rudas T. Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. 2015;42(3):832-847. doi:10.1111/sjos.12139","ista":"Klimova A, Rudas T. 2015. Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. 42(3), 832–847.","ieee":"A. Klimova and T. Rudas, “Iterative scaling in curved exponential families,” Scandinavian Journal of Statistics, vol. 42, no. 3. Wiley, pp. 832–847, 2015.","apa":"Klimova, A., & Rudas, T. (2015). Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. Wiley. https://doi.org/10.1111/sjos.12139"},"publication":"Scandinavian Journal of Statistics","date_published":"2015-09-01T00:00:00Z","scopus_import":1,"day":"01"},{"page":"261 - 269","publication":"Experimental Mathematics","citation":{"mla":"Hein, Nicolas, et al. “The Monotone Secant Conjecture in the Real Schubert Calculus.” Experimental Mathematics, vol. 24, no. 3, Taylor & Francis, 2015, pp. 261–69, doi:10.1080/10586458.2014.980044.","short":"N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, Z. Teitler, Experimental Mathematics 24 (2015) 261–269.","chicago":"Hein, Nicolas, Christopher Hillar, Abraham Martin del Campo Sanchez, Frank Sottile, and Zach Teitler. “The Monotone Secant Conjecture in the Real Schubert Calculus.” Experimental Mathematics. Taylor & Francis, 2015. https://doi.org/10.1080/10586458.2014.980044.","ama":"Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. 2015;24(3):261-269. doi:10.1080/10586458.2014.980044","ista":"Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015. The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. 24(3), 261–269.","apa":"Hein, N., Hillar, C., Martin del Campo Sanchez, A., Sottile, F., & Teitler, Z. (2015). The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2014.980044","ieee":"N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, and Z. Teitler, “The monotone secant conjecture in the real Schubert calculus,” Experimental Mathematics, vol. 24, no. 3. Taylor & Francis, pp. 261–269, 2015."},"date_published":"2015-06-23T00:00:00Z","scopus_import":1,"day":"23","article_processing_charge":"No","title":"The monotone secant conjecture in the real Schubert calculus","status":"public","intvolume":" 24","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2006","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko). We present some theoretical evidence for this conjecture, as well as computational evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of the phenomena we observed in our data. "}],"issue":"3","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.3436"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1080/10586458.2014.980044","month":"06","publication_status":"published","department":[{"_id":"CaUh"}],"publisher":"Taylor & Francis","year":"2015","date_updated":"2021-01-12T06:54:40Z","date_created":"2018-12-11T11:55:10Z","volume":24,"author":[{"last_name":"Hein","first_name":"Nicolas","full_name":"Hein, Nicolas"},{"first_name":"Christopher","last_name":"Hillar","full_name":"Hillar, Christopher"},{"first_name":"Abraham","last_name":"Martin Del Campo Sanchez","id":"4CF47F6A-F248-11E8-B48F-1D18A9856A87","full_name":"Martin Del Campo Sanchez, Abraham"},{"full_name":"Sottile, Frank","first_name":"Frank","last_name":"Sottile"},{"full_name":"Teitler, Zach","last_name":"Teitler","first_name":"Zach"}],"publist_id":"5070"},{"publist_id":"5062","issue":"7","abstract":[{"text":"The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-) faithfulness with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association.","lang":"eng"}],"type":"journal_article","author":[{"last_name":"Klimova","first_name":"Anna","id":"31934120-F248-11E8-B48F-1D18A9856A87","full_name":"Klimova, Anna"},{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","first_name":"Caroline","last_name":"Uhler","full_name":"Uhler, Caroline"},{"full_name":"Rudas, Tamás","last_name":"Rudas","first_name":"Tamás"}],"volume":87,"oa_version":"Preprint","date_updated":"2021-01-12T06:54:43Z","date_created":"2018-12-11T11:55:13Z","_id":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","department":[{"_id":"CaUh"}],"publisher":"Elsevier","intvolume":" 87","publication_status":"published","title":"Faithfulness and learning hypergraphs from discrete distributions","status":"public","month":"07","day":"01","scopus_import":1,"date_published":"2015-07-01T00:00:00Z","doi":"10.1016/j.csda.2015.01.017","language":[{"iso":"eng"}],"citation":{"ieee":"A. Klimova, C. Uhler, and T. Rudas, “Faithfulness and learning hypergraphs from discrete distributions,” Computational Statistics & Data Analysis, vol. 87, no. 7. Elsevier, pp. 57–72, 2015.","apa":"Klimova, A., Uhler, C., & Rudas, T. (2015). Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. Elsevier. https://doi.org/10.1016/j.csda.2015.01.017","ista":"Klimova A, Uhler C, Rudas T. 2015. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. 87(7), 57–72.","ama":"Klimova A, Uhler C, Rudas T. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. 2015;87(7):57-72. doi:10.1016/j.csda.2015.01.017","chicago":"Klimova, Anna, Caroline Uhler, and Tamás Rudas. “Faithfulness and Learning Hypergraphs from Discrete Distributions.” Computational Statistics & Data Analysis. Elsevier, 2015. https://doi.org/10.1016/j.csda.2015.01.017.","short":"A. Klimova, C. Uhler, T. Rudas, Computational Statistics & Data Analysis 87 (2015) 57–72.","mla":"Klimova, Anna, et al. “Faithfulness and Learning Hypergraphs from Discrete Distributions.” Computational Statistics & Data Analysis, vol. 87, no. 7, Elsevier, 2015, pp. 57–72, doi:10.1016/j.csda.2015.01.017."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1404.6617"}],"oa":1,"publication":"Computational Statistics & Data Analysis","page":"57 - 72","quality_controlled":"1"},{"type":"journal_article","abstract":[{"text":"The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in the same part. If the restrictions are too harsh, then the topological Tverberg theorem fails. The colored Tverberg theorem corresponds to graphs constructed as disjoint unions of small complete graphs. Hell studied the case of paths and cycles. In graph theory these partitions are usually viewed as graph colorings. As explored by Aharoni, Haxell, Meshulam and others there are fundamental connections between several notions of graph colorings and topological combinatorics. For ordinary graph colorings it is enough to require that the number of colors q satisfy q>Δ, where Δ is the maximal degree of the graph. It was proven by the first author using equivariant topology that if q>Δ 2 then the topological Tverberg theorem still works. It is conjectured that q>KΔ is also enough for some constant K, and in this paper we prove a fixed-parameter version of that conjecture. The required topological connectivity results are proven with shellability, which also strengthens some previous partial results where the topological connectivity was proven with the nerve lemma.","lang":"eng"}],"publist_id":"5183","issue":"1","status":"public","publication_status":"published","title":"Tverberg's Theorem and Graph Coloring","publisher":"Springer","intvolume":" 51","department":[{"_id":"CaUh"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"1911","year":"2014","acknowledgement":"Patrik Norén gratefully acknowledges support from the Wallenberg foundation","date_created":"2018-12-11T11:54:40Z","date_updated":"2021-01-12T06:54:01Z","oa_version":"None","volume":51,"author":[{"full_name":"Engström, Alexander","last_name":"Engström","first_name":"Alexander"},{"full_name":"Noren, Patrik","last_name":"Noren","first_name":"Patrik","id":"46870C74-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":1,"month":"01","day":"01","page":"207 - 220","publication":"Discrete & Computational Geometry","citation":{"short":"A. Engström, P. Noren, Discrete & Computational Geometry 51 (2014) 207–220.","mla":"Engström, Alexander, and Patrik Noren. “Tverberg’s Theorem and Graph Coloring.” Discrete & Computational Geometry, vol. 51, no. 1, Springer, 2014, pp. 207–20, doi:10.1007/s00454-013-9556-3.","chicago":"Engström, Alexander, and Patrik Noren. “Tverberg’s Theorem and Graph Coloring.” Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-013-9556-3.","ama":"Engström A, Noren P. Tverberg’s Theorem and Graph Coloring. Discrete & Computational Geometry. 2014;51(1):207-220. doi:10.1007/s00454-013-9556-3","apa":"Engström, A., & Noren, P. (2014). Tverberg’s Theorem and Graph Coloring. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9556-3","ieee":"A. Engström and P. Noren, “Tverberg’s Theorem and Graph Coloring,” Discrete & Computational Geometry, vol. 51, no. 1. Springer, pp. 207–220, 2014.","ista":"Engström A, Noren P. 2014. Tverberg’s Theorem and Graph Coloring. Discrete & Computational Geometry. 51(1), 207–220."},"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.1007/s00454-013-9556-3"},{"day":"01","month":"08","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2014-08-01T00:00:00Z","doi":"10.1016/j.jbi.2014.01.008","quality_controlled":"1","page":"133 - 141","publication":"Journal of Biomedical Informatics","main_file_link":[{"url":"http://arxiv.org/abs/1401.5193","open_access":"1"}],"oa":1,"citation":{"mla":"Yu, Fei, et al. “Scalable Privacy-Preserving Data Sharing Methodology for Genome-Wide Association Studies.” Journal of Biomedical Informatics, vol. 50, Elsevier, 2014, pp. 133–41, doi:10.1016/j.jbi.2014.01.008.","short":"F. Yu, S. Fienberg, A. Slaković, C. Uhler, Journal of Biomedical Informatics 50 (2014) 133–141.","chicago":"Yu, Fei, Stephen Fienberg, Alexandra Slaković, and Caroline Uhler. “Scalable Privacy-Preserving Data Sharing Methodology for Genome-Wide Association Studies.” Journal of Biomedical Informatics. Elsevier, 2014. https://doi.org/10.1016/j.jbi.2014.01.008.","ama":"Yu F, Fienberg S, Slaković A, Uhler C. Scalable privacy-preserving data sharing methodology for genome-wide association studies. Journal of Biomedical Informatics. 2014;50:133-141. doi:10.1016/j.jbi.2014.01.008","ista":"Yu F, Fienberg S, Slaković A, Uhler C. 2014. Scalable privacy-preserving data sharing methodology for genome-wide association studies. Journal of Biomedical Informatics. 50, 133–141.","apa":"Yu, F., Fienberg, S., Slaković, A., & Uhler, C. (2014). Scalable privacy-preserving data sharing methodology for genome-wide association studies. Journal of Biomedical Informatics. Elsevier. https://doi.org/10.1016/j.jbi.2014.01.008","ieee":"F. Yu, S. Fienberg, A. Slaković, and C. Uhler, “Scalable privacy-preserving data sharing methodology for genome-wide association studies,” Journal of Biomedical Informatics, vol. 50. Elsevier, pp. 133–141, 2014."},"abstract":[{"text":"The protection of privacy of individual-level information in genome-wide association study (GWAS) databases has been a major concern of researchers following the publication of “an attack” on GWAS data by Homer et al. (2008). Traditional statistical methods for confidentiality and privacy protection of statistical databases do not scale well to deal with GWAS data, 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 that 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, Uhler et al. (2013) proposed new methods to release aggregate GWAS data without compromising an individual’s privacy. We extend the methods developed in Uhler et al. (2013) for releasing differentially-private χ2χ2-statistics by allowing for arbitrary number of cases and controls, and for releasing differentially-private allelic test statistics. We also provide a new interpretation by assuming the controls’ data are known, which is a realistic assumption because some GWAS use publicly available data as controls. We assess the performance of the proposed methods through a risk-utility analysis on a real data set consisting of DNA samples collected by the Wellcome Trust Case Control Consortium and compare the methods with the differentially-private release mechanism proposed by Johnson and Shmatikov (2013).","lang":"eng"}],"publist_id":"5065","type":"journal_article","date_updated":"2021-01-12T06:54:42Z","date_created":"2018-12-11T11:55:12Z","oa_version":"Submitted Version","volume":50,"author":[{"full_name":"Yu, Fei","first_name":"Fei","last_name":"Yu"},{"first_name":"Stephen","last_name":"Fienberg","full_name":"Fienberg, Stephen"},{"full_name":"Slaković, Alexandra","first_name":"Alexandra","last_name":"Slaković"},{"full_name":"Uhler, Caroline","first_name":"Caroline","last_name":"Uhler","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216"}],"status":"public","publication_status":"published","title":"Scalable privacy-preserving data sharing methodology for genome-wide association studies","publisher":"Elsevier","department":[{"_id":"CaUh"}],"intvolume":" 50","year":"2014","_id":"2011","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This research was partially supported by NSF Awards EMSW21-RTG and BCS-0941518 to the Department of Statistics at Carnegie Mellon University, and by NSF Grant BCS-0941553 to the Department of Statistics at Pennsylvania State University. This work was also supported in part by the National Center for Research Resources, Grant UL1 RR033184, and is now at the National Center for Advancing Translational Sciences, Grant UL1 TR000127 to Pennsylvania State University. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NSF and NIH."},{"article_processing_charge":"No","month":"03","day":"20","oa":1,"citation":{"chicago":"Klimova, Anna, and Tamás Rudas. “GIPFrm: Generalized Iterative Proportional Fitting for Relational Models.” The Comprehensive R Archive Network, 2014.","mla":"Klimova, Anna, and Tamás Rudas. GIPFrm: Generalized Iterative Proportional Fitting for Relational Models. The Comprehensive R Archive Network, 2014.","short":"A. Klimova, T. Rudas, (2014).","ista":"Klimova A, Rudas T. 2014. gIPFrm: Generalized iterative proportional fitting for relational models, The Comprehensive R Archive Network.","ieee":"A. Klimova and T. Rudas, “gIPFrm: Generalized iterative proportional fitting for relational models.” The Comprehensive R Archive Network, 2014.","apa":"Klimova, A., & Rudas, T. (2014). gIPFrm: Generalized iterative proportional fitting for relational models. The Comprehensive R Archive Network.","ama":"Klimova A, Rudas T. gIPFrm: Generalized iterative proportional fitting for relational models. 2014."},"main_file_link":[{"open_access":"1","url":"https://CRAN.R-project.org/package=gIPFrm "}],"date_published":"2014-03-20T00:00:00Z","type":"research_data_reference","publist_id":"5069","abstract":[{"text":"Maximum likelihood estimation under relational models, with or without the overall effect. For more information see the reference manual","lang":"eng"}],"_id":"2007","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2014","department":[{"_id":"CaUh"}],"publisher":"The Comprehensive R Archive Network","status":"public","title":"gIPFrm: Generalized iterative proportional fitting for relational models","author":[{"full_name":"Klimova, Anna","id":"31934120-F248-11E8-B48F-1D18A9856A87","last_name":"Klimova","first_name":"Anna"},{"last_name":"Rudas","first_name":"Tamás","full_name":"Rudas, Tamás"}],"oa_version":"Published Version","date_updated":"2022-08-26T08:12:12Z","date_created":"2018-12-11T11:55:10Z"},{"publist_id":"5063","publication_status":"published","publisher":"Springer","department":[{"_id":"CaUh"}],"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).","date_created":"2018-12-11T11:55:12Z","date_updated":"2021-01-12T06:54:43Z","volume":14,"author":[{"first_name":"Shaowei","last_name":"Lin","full_name":"Lin, Shaowei"},{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","first_name":"Caroline","last_name":"Uhler","full_name":"Uhler, Caroline"},{"full_name":"Sturmfels, Bernd","last_name":"Sturmfels","first_name":"Bernd"},{"full_name":"Bühlmann, Peter","last_name":"Bühlmann","first_name":"Peter"}],"month":"10","quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1209.0285"}],"language":[{"iso":"eng"}],"doi":"10.1007/s10208-014-9205-0","type":"journal_article","abstract":[{"lang":"eng","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"}],"issue":"5","status":"public","title":"Hypersurfaces and their singularities in partial correlation testing","intvolume":" 14","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2013","oa_version":"Submitted Version","scopus_import":1,"day":"10","page":"1079 - 1116","publication":"Foundations of Computational Mathematics","citation":{"ama":"Lin S, Uhler C, Sturmfels B, Bühlmann P. Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. 2014;14(5):1079-1116. doi:10.1007/s10208-014-9205-0","apa":"Lin, S., Uhler, C., Sturmfels, B., & Bühlmann, P. (2014). Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9205-0","ieee":"S. Lin, C. Uhler, B. Sturmfels, and P. Bühlmann, “Hypersurfaces and their singularities in partial correlation testing,” Foundations of Computational Mathematics, 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.","short":"S. Lin, C. Uhler, B. Sturmfels, P. Bühlmann, Foundations of Computational Mathematics 14 (2014) 1079–1116.","mla":"Lin, Shaowei, et al. “Hypersurfaces and Their Singularities in Partial Correlation Testing.” Foundations of Computational Mathematics, vol. 14, no. 5, Springer, 2014, pp. 1079–116, doi:10.1007/s10208-014-9205-0.","chicago":"Lin, Shaowei, Caroline Uhler, Bernd Sturmfels, and Peter Bühlmann. “Hypersurfaces and Their Singularities in Partial Correlation Testing.” Foundations of Computational Mathematics. Springer, 2014. https://doi.org/10.1007/s10208-014-9205-0."},"date_published":"2014-10-10T00:00:00Z"},{"publist_id":"5004","author":[{"full_name":"Yu, Fei","last_name":"Yu","first_name":"Fei"},{"first_name":"Michal","last_name":"Rybar","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","full_name":"Rybar, Michal"},{"first_name":"Caroline","last_name":"Uhler","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","full_name":"Uhler, Caroline"},{"full_name":"Fienberg, Stephen","last_name":"Fienberg","first_name":"Stephen"}],"date_created":"2018-12-11T11:55:24Z","date_updated":"2021-01-12T06:54:57Z","volume":8744,"acknowledgement":"This research was partially supported by BCS- 0941518 to the Department of Statistics at Carnegie Mellon University.","year":"2014","publication_status":"published","editor":[{"full_name":"Domingo Ferrer, Josep","last_name":"Domingo Ferrer","first_name":"Josep"}],"department":[{"_id":"KrPi"},{"_id":"CaUh"}],"publisher":"Springer","month":"01","conference":{"start_date":"2014-09-17","location":"Ibiza, Spain","end_date":"2014-09-19","name":"PSD: Privacy in Statistical Databases"},"doi":"10.1007/978-3-319-11257-2_14","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1407.8067"}],"external_id":{"arxiv":["1407.8067"]},"quality_controlled":"1","project":[{"name":"ROOTS Genome-wide Analysis of Root Traits","_id":"25636330-B435-11E9-9278-68D0E5697425","grant_number":"11-NSF-1070"}],"abstract":[{"text":"Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems with convex penalty functions and selecting the penalty parameters by cross-validation. In particular, we focus on penalized logistic regression with elastic-net regularization, a method widely used to in GWAS analyses to identify disease-causing genes. We show how a differentially private procedure for penalized logistic regression with elastic-net regularization can be applied to the analysis of GWAS data and evaluate our method’s performance.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"Submitted Version","_id":"2047","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases","intvolume":" 8744","day":"01","scopus_import":1,"date_published":"2014-01-01T00:00:00Z","publication":"Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)","citation":{"chicago":"Yu, Fei, Michal Rybar, Caroline Uhler, and Stephen Fienberg. “Differentially-Private Logistic Regression for Detecting Multiple-SNP Association in GWAS Databases.” In Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), edited by Josep Domingo Ferrer, 8744:170–84. Springer, 2014. https://doi.org/10.1007/978-3-319-11257-2_14.","mla":"Yu, Fei, et al. “Differentially-Private Logistic Regression for Detecting Multiple-SNP Association in GWAS Databases.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), edited by Josep Domingo Ferrer, vol. 8744, Springer, 2014, pp. 170–84, doi:10.1007/978-3-319-11257-2_14.","short":"F. Yu, M. Rybar, C. Uhler, S. Fienberg, in:, J. Domingo Ferrer (Ed.), Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer, 2014, pp. 170–184.","ista":"Yu F, Rybar M, Uhler C, Fienberg S. 2014. Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PSD: Privacy in Statistical Databases, LNCS, vol. 8744, 170–184.","apa":"Yu, F., Rybar, M., Uhler, C., & Fienberg, S. (2014). Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases. In J. Domingo Ferrer (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8744, pp. 170–184). Ibiza, Spain: Springer. https://doi.org/10.1007/978-3-319-11257-2_14","ieee":"F. Yu, M. Rybar, C. Uhler, and S. Fienberg, “Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Ibiza, Spain, 2014, vol. 8744, pp. 170–184.","ama":"Yu F, Rybar M, Uhler C, Fienberg S. Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases. In: Domingo Ferrer J, ed. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol 8744. Springer; 2014:170-184. doi:10.1007/978-3-319-11257-2_14"},"page":"170 - 184"},{"date_created":"2018-12-11T11:56:10Z","date_updated":"2021-01-12T06:55:48Z","volume":55,"author":[{"full_name":"Haws, David","last_name":"Haws","first_name":"David"},{"full_name":"Martin Del Campo Sanchez, Abraham","last_name":"Martin Del Campo Sanchez","first_name":"Abraham","id":"4CF47F6A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Takemura, Akimichi","last_name":"Takemura","first_name":"Akimichi"},{"full_name":"Yoshida, Ruriko","last_name":"Yoshida","first_name":"Ruriko"}],"publication_status":"published","publisher":"Springer","department":[{"_id":"CaUh"}],"year":"2014","acknowledgement":"Research of Martín del Campo supported in part by NSF Grant DMS-915211.","publist_id":"4804","language":[{"iso":"eng"}],"doi":"10.1007/s13366-013-0178-y","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1204.3070","open_access":"1"}],"oa":1,"month":"03","oa_version":"Submitted Version","title":"Markov degree of the three-state toric homogeneous Markov chain model","status":"public","intvolume":" 55","_id":"2178","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We consider the three-state toric homogeneous Markov chain model (THMC) without loops and initial parameters. At time T, the size of the design matrix is 6 × 3 · 2T-1 and the convex hull of its columns is the model polytope. We study the behavior of this polytope for T ≥ 3 and we show that it is defined by 24 facets for all T ≥ 5. Moreover, we give a complete description of these facets. From this, we deduce that the toric ideal associated with the design matrix is generated by binomials of degree at most 6. Our proof is based on a result due to Sturmfels, who gave a bound on the degree of the generators of a toric ideal, provided the normality of the corresponding toric variety. In our setting, we established the normality of the toric variety associated to the THMC model by studying the geometric properties of the model polytope.","lang":"eng"}],"issue":"1","type":"journal_article","date_published":"2014-03-01T00:00:00Z","page":"161 - 188","publication":"Beitrage zur Algebra und Geometrie","citation":{"chicago":"Haws, David, Abraham Martin del Campo Sanchez, Akimichi Takemura, and Ruriko Yoshida. “Markov Degree of the Three-State Toric Homogeneous Markov Chain Model.” Beitrage Zur Algebra Und Geometrie. Springer, 2014. https://doi.org/10.1007/s13366-013-0178-y.","mla":"Haws, David, et al. “Markov Degree of the Three-State Toric Homogeneous Markov Chain Model.” Beitrage Zur Algebra Und Geometrie, vol. 55, no. 1, Springer, 2014, pp. 161–88, doi:10.1007/s13366-013-0178-y.","short":"D. Haws, A. Martin del Campo Sanchez, A. Takemura, R. Yoshida, Beitrage Zur Algebra Und Geometrie 55 (2014) 161–188.","ista":"Haws D, Martin del Campo Sanchez A, Takemura A, Yoshida R. 2014. Markov degree of the three-state toric homogeneous Markov chain model. Beitrage zur Algebra und Geometrie. 55(1), 161–188.","ieee":"D. Haws, A. Martin del Campo Sanchez, A. Takemura, and R. Yoshida, “Markov degree of the three-state toric homogeneous Markov chain model,” Beitrage zur Algebra und Geometrie, vol. 55, no. 1. Springer, pp. 161–188, 2014.","apa":"Haws, D., Martin del Campo Sanchez, A., Takemura, A., & Yoshida, R. (2014). Markov degree of the three-state toric homogeneous Markov chain model. Beitrage Zur Algebra Und Geometrie. Springer. https://doi.org/10.1007/s13366-013-0178-y","ama":"Haws D, Martin del Campo Sanchez A, Takemura A, Yoshida R. Markov degree of the three-state toric homogeneous Markov chain model. Beitrage zur Algebra und Geometrie. 2014;55(1):161-188. doi:10.1007/s13366-013-0178-y"},"day":"01","scopus_import":1},{"department":[{"_id":"HeEd"},{"_id":"CaUh"}],"publication_status":"submitted","status":"public","title":"Sphere packing with limited overlap","_id":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper. The second author has been supported by the Max Planck Center for Visual Computing and Communication","year":"2014","oa_version":"Submitted Version","date_created":"2018-12-11T11:55:12Z","date_updated":"2023-10-18T08:06:45Z","author":[{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-8030-9299","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"},{"first_name":"Caroline","last_name":"Uhler","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","full_name":"Uhler, Caroline"}],"type":"preprint","article_number":"1401.0468","publist_id":"5064","abstract":[{"lang":"eng","text":"The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice."}],"main_file_link":[{"open_access":"1","url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf"}],"citation":{"ista":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.","apa":"Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468","ieee":"M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. .","ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/arXiv.1401.0468","chicago":"Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.)."},"oa":1,"external_id":{"arxiv":["1401.0468"]},"publication":"arXiv","language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.48550/arXiv.1401.0468","article_processing_charge":"No","month":"01","day":"01"},{"volume":41,"date_created":"2018-12-11T11:55:11Z","date_updated":"2021-01-12T06:54:42Z","author":[{"orcid":"0000-0002-7008-0216","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","last_name":"Uhler","first_name":"Caroline","full_name":"Uhler, Caroline"},{"full_name":"Raskutti, Garvesh","last_name":"Raskutti","first_name":"Garvesh"},{"full_name":"Bühlmann, Peter","first_name":"Peter","last_name":"Bühlmann"},{"full_name":"Yu, Bin","last_name":"Yu","first_name":"Bin"}],"department":[{"_id":"CaUh"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","year":"2013","publist_id":"5066","language":[{"iso":"eng"}],"doi":"10.1214/12-AOS1080","quality_controlled":"1","external_id":{"arxiv":["1207.0547"]},"main_file_link":[{"open_access":"1","url":"www.doi.org/10.1214/12-AOS1080"}],"oa":1,"month":"04","oa_version":"Published Version","intvolume":" 41","title":"Geometry of the faithfulness assumption in causal inference","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2010","issue":"2","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"}],"type":"journal_article","date_published":"2013-04-01T00:00:00Z","page":"436 - 463","citation":{"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.","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","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.","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","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.","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."},"publication":"The Annals of Statistics","day":"01","scopus_import":1},{"article_processing_charge":"No","day":"01","month":"08","main_file_link":[{"url":"http://repository.cmu.edu/jpc/vol5/iss1/6","open_access":"1"}],"oa":1,"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","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.","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.","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","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.","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."},"publication":"Journal of Privacy and Confidentiality ","page":"137 - 166","quality_controlled":"1","doi":"10.29012/jpc.v5i1.629","date_published":"2013-08-01T00:00:00Z","language":[{"iso":"eng"}],"type":"journal_article","issue":"1","publist_id":"5067","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"}],"_id":"2009","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2013","department":[{"_id":"CaUh"}],"publisher":"Carnegie Mellon University","intvolume":" 5","status":"public","title":"Privacy-preserving data sharing for genome-wide association studies","publication_status":"published","author":[{"orcid":"0000-0002-7008-0216","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","last_name":"Uhler","first_name":"Caroline","full_name":"Uhler, Caroline"},{"full_name":"Slavkovic, Aleksandra","first_name":"Aleksandra","last_name":"Slavkovic"},{"first_name":"Stephen","last_name":"Fienberg","full_name":"Fienberg, Stephen"}],"volume":5,"oa_version":"Published Version","date_updated":"2021-01-12T06:54:41Z","date_created":"2018-12-11T11:55:11Z"},{"day":"07","scopus_import":1,"date_published":"2013-11-07T00:00:00Z","publication":"SIAM Review","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.","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.","ama":"Uhler C, Wright S. Packing ellipsoids with overlap. SIAM Review. 2013;55(4):671-706. doi:10.1137/120872309","ista":"Uhler C, Wright S. 2013. Packing ellipsoids with overlap. SIAM Review. 55(4), 671–706.","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.","apa":"Uhler, C., & Wright, S. (2013). Packing ellipsoids with overlap. SIAM Review. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/120872309"},"page":"671 - 706","abstract":[{"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.","lang":"eng"}],"issue":"4","type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2280","status":"public","title":"Packing ellipsoids with overlap","intvolume":" 55","month":"11","doi":"10.1137/120872309","language":[{"iso":"eng"}],"external_id":{"arxiv":["1204.0235"]},"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1204.0235"}],"quality_controlled":"1","publist_id":"4655","author":[{"full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","last_name":"Uhler","first_name":"Caroline"},{"last_name":"Wright","first_name":"Stephen","full_name":"Wright, Stephen"}],"date_created":"2018-12-11T11:56:44Z","date_updated":"2021-01-12T06:56:30Z","volume":55,"year":"2013","publication_status":"published","department":[{"_id":"CaUh"}],"publisher":"Society for Industrial and Applied Mathematics "},{"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","year":"2012","publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"CaUh"}],"author":[{"full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","last_name":"Uhler","first_name":"Caroline"}],"date_updated":"2021-01-12T07:40:04Z","date_created":"2018-12-11T12:00:33Z","volume":40,"publist_id":"3767","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1012.2643"}],"quality_controlled":"1","doi":"10.1214/11-AOS957","language":[{"iso":"eng"}],"month":"02","_id":"2959","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Geometry of maximum likelihood estimation in Gaussian graphical models","intvolume":" 40","oa_version":"Preprint","type":"journal_article","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"}],"issue":"1","publication":"Annals of Statistics","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","ista":"Uhler C. 2012. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 40(1), 238–261.","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","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.","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.","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."},"page":"238 - 261","date_published":"2012-02-01T00:00:00Z","scopus_import":1,"day":"01"}]