--- _id: '2008' 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. 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). author: - first_name: Anna full_name: Klimova, Anna id: 31934120-F248-11E8-B48F-1D18A9856A87 last_name: Klimova - first_name: Tamás full_name: Rudas, Tamás last_name: Rudas citation: 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 apa: Klimova, A., & Rudas, T. (2015). Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. Wiley. https://doi.org/10.1111/sjos.12139 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. 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. ista: Klimova A, Rudas T. 2015. Iterative scaling in curved exponential families. Scandinavian Journal of Statistics. 42(3), 832–847. 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. date_created: 2018-12-11T11:55:11Z date_published: 2015-09-01T00:00:00Z date_updated: 2021-01-12T06:54:41Z day: '01' department: - _id: CaUh doi: 10.1111/sjos.12139 intvolume: ' 42' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1307.3282 month: '09' oa: 1 oa_version: Preprint page: 832 - 847 publication: Scandinavian Journal of Statistics publication_status: published publisher: Wiley publist_id: '5068' quality_controlled: '1' scopus_import: 1 status: public title: Iterative scaling in curved exponential families type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 42 year: '2015' ... --- _id: '2006' 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. ' article_processing_charge: No author: - first_name: Nicolas full_name: Hein, Nicolas last_name: Hein - first_name: Christopher full_name: Hillar, Christopher last_name: Hillar - first_name: Abraham full_name: Martin Del Campo Sanchez, Abraham id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87 last_name: Martin Del Campo Sanchez - first_name: Frank full_name: Sottile, Frank last_name: Sottile - first_name: Zach full_name: Teitler, Zach last_name: Teitler citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:55:10Z date_published: 2015-06-23T00:00:00Z date_updated: 2021-01-12T06:54:40Z day: '23' department: - _id: CaUh doi: 10.1080/10586458.2014.980044 intvolume: ' 24' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.3436 month: '06' oa: 1 oa_version: Preprint page: 261 - 269 publication: Experimental Mathematics publication_status: published publisher: Taylor & Francis publist_id: '5070' quality_controlled: '1' scopus_import: 1 status: public title: The monotone secant conjecture in the real Schubert calculus type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2015' ... --- _id: '2014' abstract: - lang: eng 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. author: - first_name: Anna full_name: Klimova, Anna id: 31934120-F248-11E8-B48F-1D18A9856A87 last_name: Klimova - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Tamás full_name: Rudas, Tamás last_name: Rudas citation: 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 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 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. 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. ista: Klimova A, Uhler C, Rudas T. 2015. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. 87(7), 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. short: A. Klimova, C. Uhler, T. Rudas, Computational Statistics & Data Analysis 87 (2015) 57–72. date_created: 2018-12-11T11:55:13Z date_published: 2015-07-01T00:00:00Z date_updated: 2021-01-12T06:54:43Z day: '01' department: - _id: CaUh doi: 10.1016/j.csda.2015.01.017 intvolume: ' 87' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1404.6617 month: '07' oa: 1 oa_version: Preprint page: 57 - 72 publication: Computational Statistics & Data Analysis publication_status: published publisher: Elsevier publist_id: '5062' quality_controlled: '1' scopus_import: 1 status: public title: Faithfulness and learning hypergraphs from discrete distributions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 87 year: '2015' ... --- _id: '1911' abstract: - lang: eng 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. acknowledgement: Patrik Norén gratefully acknowledges support from the Wallenberg foundation author: - first_name: Alexander full_name: Engström, Alexander last_name: Engström - first_name: Patrik full_name: Noren, Patrik id: 46870C74-F248-11E8-B48F-1D18A9856A87 last_name: Noren citation: 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 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. 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. 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. short: A. Engström, P. Noren, Discrete & Computational Geometry 51 (2014) 207–220. date_created: 2018-12-11T11:54:40Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T06:54:01Z day: '01' department: - _id: CaUh doi: 10.1007/s00454-013-9556-3 intvolume: ' 51' issue: '1' language: - iso: eng month: '01' oa_version: None page: 207 - 220 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '5183' scopus_import: 1 status: public title: Tverberg's Theorem and Graph Coloring type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 51 year: '2014' ... --- _id: '2011' abstract: - lang: eng 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). 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. author: - first_name: Fei full_name: Yu, Fei last_name: Yu - first_name: Stephen full_name: Fienberg, Stephen last_name: Fienberg - first_name: Alexandra full_name: Slaković, Alexandra last_name: Slaković - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:55:12Z date_published: 2014-08-01T00:00:00Z date_updated: 2021-01-12T06:54:42Z day: '01' department: - _id: CaUh doi: 10.1016/j.jbi.2014.01.008 intvolume: ' 50' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1401.5193 month: '08' oa: 1 oa_version: Submitted Version page: 133 - 141 publication: Journal of Biomedical Informatics publication_status: published publisher: Elsevier publist_id: '5065' quality_controlled: '1' scopus_import: 1 status: public title: Scalable privacy-preserving data sharing methodology for genome-wide association studies type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 50 year: '2014' ...