--- _id: '698' abstract: - lang: eng text: 'Extracellular matrix signals from the microenvironment regulate gene expression patterns and cell behavior. Using a combination of experiments and geometric models, we demonstrate correlations between cell geometry, three-dimensional (3D) organization of chromosome territories, and gene expression. Fluorescence in situ hybridization experiments showed that micropatterned fibroblasts cultured on anisotropic versus isotropic substrates resulted in repositioning of specific chromosomes, which contained genes that were differentially regulated by cell geometries. Experiments combined with ellipsoid packing models revealed that the mechanosensitivity of chromosomes was correlated with their orientation in the nucleus. Transcription inhibition experiments suggested that the intermingling degree was more sensitive to global changes in transcription than to chromosome radial positioning and its orientations. These results suggested that cell geometry modulated 3D chromosome arrangement, and their neighborhoods correlated with gene expression patterns in a predictable manner. This is central to understanding geometric control of genetic programs involved in cellular homeostasis and the associated diseases. ' author: - first_name: Yejun full_name: Wang, Yejun last_name: Wang - first_name: Mallika full_name: Nagarajan, Mallika last_name: Nagarajan - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Gv full_name: Shivashankar, Gv last_name: Shivashankar citation: ama: Wang Y, Nagarajan M, Uhler C, Shivashankar G. Orientation and repositioning of chromosomes correlate with cell geometry dependent gene expression. Molecular Biology of the Cell. 2017;28(14):1997-2009. doi:10.1091/mbc.E16-12-0825 apa: Wang, Y., Nagarajan, M., Uhler, C., & Shivashankar, G. (2017). Orientation and repositioning of chromosomes correlate with cell geometry dependent gene expression. Molecular Biology of the Cell. American Society for Cell Biology. https://doi.org/10.1091/mbc.E16-12-0825 chicago: Wang, Yejun, Mallika Nagarajan, Caroline Uhler, and Gv Shivashankar. “Orientation and Repositioning of Chromosomes Correlate with Cell Geometry Dependent Gene Expression.” Molecular Biology of the Cell. American Society for Cell Biology, 2017. https://doi.org/10.1091/mbc.E16-12-0825. ieee: Y. Wang, M. Nagarajan, C. Uhler, and G. Shivashankar, “Orientation and repositioning of chromosomes correlate with cell geometry dependent gene expression,” Molecular Biology of the Cell, vol. 28, no. 14. American Society for Cell Biology, pp. 1997–2009, 2017. ista: Wang Y, Nagarajan M, Uhler C, Shivashankar G. 2017. Orientation and repositioning of chromosomes correlate with cell geometry dependent gene expression. Molecular Biology of the Cell. 28(14), 1997–2009. mla: Wang, Yejun, et al. “Orientation and Repositioning of Chromosomes Correlate with Cell Geometry Dependent Gene Expression.” Molecular Biology of the Cell, vol. 28, no. 14, American Society for Cell Biology, 2017, pp. 1997–2009, doi:10.1091/mbc.E16-12-0825. short: Y. Wang, M. Nagarajan, C. Uhler, G. Shivashankar, Molecular Biology of the Cell 28 (2017) 1997–2009. date_created: 2018-12-11T11:47:59Z date_published: 2017-07-07T00:00:00Z date_updated: 2021-01-12T08:11:17Z day: '07' ddc: - '519' department: - _id: CaUh doi: 10.1091/mbc.E16-12-0825 file: - access_level: open_access checksum: de01dac9e30970cfa6ae902480a4e04d content_type: application/pdf creator: system date_created: 2018-12-12T10:10:53Z date_updated: 2020-07-14T12:47:46Z file_id: '4844' file_name: IST-2017-892-v1+1_Mol._Biol._Cell-2017-Wang-1997-2009.pdf file_size: 1086097 relation: main_file file_date_updated: 2020-07-14T12:47:46Z has_accepted_license: '1' intvolume: ' 28' issue: '14' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '07' oa: 1 oa_version: Published Version page: 1997 - 2009 project: - _id: 2530CA10-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Y 903-N35 name: 'Gaussian Graphical Models: Theory and Applications' publication: Molecular Biology of the Cell publication_identifier: issn: - '10591524' publication_status: published publisher: American Society for Cell Biology publist_id: '7001' pubrep_id: '892' quality_controlled: '1' scopus_import: 1 status: public title: Orientation and repositioning of chromosomes correlate with cell geometry dependent gene expression tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2017' ... --- _id: '1208' abstract: - lang: eng text: We study parameter estimation in linear Gaussian covariance models, which are p-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill climbing method to converge to the global maximum. Although we are primarily interested in the case in which n≫p, the proofs of our results utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably, our numerical simulations indicate that our results remain valid for p as small as 2. An important consequence of this analysis is that, for sample sizes n≃14p, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem. © 2016 The Royal Statistical Society and Blackwell Publishing Ltd. article_processing_charge: No author: - first_name: Piotr full_name: Zwiernik, Piotr last_name: Zwiernik - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Donald full_name: Richards, Donald last_name: Richards citation: ama: 'Zwiernik P, Uhler C, Richards D. Maximum likelihood estimation for linear Gaussian covariance models. Journal of the Royal Statistical Society Series B: Statistical Methodology. 2017;79(4):1269-1292. doi:10.1111/rssb.12217' apa: 'Zwiernik, P., Uhler, C., & Richards, D. (2017). Maximum likelihood estimation for linear Gaussian covariance models. Journal of the Royal Statistical Society. Series B: Statistical Methodology. Wiley-Blackwell. https://doi.org/10.1111/rssb.12217' chicago: 'Zwiernik, Piotr, Caroline Uhler, and Donald Richards. “Maximum Likelihood Estimation for Linear Gaussian Covariance Models.” Journal of the Royal Statistical Society. Series B: Statistical Methodology. Wiley-Blackwell, 2017. https://doi.org/10.1111/rssb.12217.' ieee: 'P. Zwiernik, C. Uhler, and D. Richards, “Maximum likelihood estimation for linear Gaussian covariance models,” Journal of the Royal Statistical Society. Series B: Statistical Methodology, vol. 79, no. 4. Wiley-Blackwell, pp. 1269–1292, 2017.' ista: 'Zwiernik P, Uhler C, Richards D. 2017. Maximum likelihood estimation for linear Gaussian covariance models. Journal of the Royal Statistical Society. Series B: Statistical Methodology. 79(4), 1269–1292.' mla: 'Zwiernik, Piotr, et al. “Maximum Likelihood Estimation for Linear Gaussian Covariance Models.” Journal of the Royal Statistical Society. Series B: Statistical Methodology, vol. 79, no. 4, Wiley-Blackwell, 2017, pp. 1269–92, doi:10.1111/rssb.12217.' short: 'P. Zwiernik, C. Uhler, D. Richards, Journal of the Royal Statistical Society. Series B: Statistical Methodology 79 (2017) 1269–1292.' date_created: 2018-12-11T11:50:43Z date_published: 2017-09-01T00:00:00Z date_updated: 2023-09-20T11:17:21Z day: '01' department: - _id: CaUh doi: 10.1111/rssb.12217 external_id: isi: - '000411712300012' intvolume: ' 79' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1408.5604 month: '09' oa: 1 oa_version: Submitted Version page: 1269 - 1292 project: - _id: 2530CA10-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Y 903-N35 name: 'Gaussian Graphical Models: Theory and Applications' publication: 'Journal of the Royal Statistical Society. Series B: Statistical Methodology' publication_identifier: issn: - '13697412' publication_status: published publisher: Wiley-Blackwell publist_id: '6142' quality_controlled: '1' scopus_import: '1' status: public title: Maximum likelihood estimation for linear Gaussian covariance models type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 79 year: '2017' ... --- _id: '1168' abstract: - lang: eng text: Optimum experimental design theory has recently been extended for parameter estimation in copula models. The use of these models allows one to gain in flexibility by considering the model parameter set split into marginal and dependence parameters. However, this separation also leads to the natural issue of estimating only a subset of all model parameters. In this work, we treat this problem with the application of the (Formula presented.)-optimality to copula models. First, we provide an extension of the corresponding equivalence theory. Then, we analyze a wide range of flexible copula models to highlight the usefulness of (Formula presented.)-optimality in many possible scenarios. Finally, we discuss how the usage of the introduced design criterion also relates to the more general issue of copula selection and optimal design for model discrimination. acknowledgement: 'This work has been supported by the project ANR-2011-IS01-001-01 “DESIRE” and Austrian Science Fund (FWF) I833-N18. Open access funding is provided by the Austrian Science Fund (FWF). ' article_processing_charge: No author: - first_name: Elisa full_name: Perrone, Elisa id: 2A5F8724-F248-11E8-B48F-1D18A9856A87 last_name: Perrone orcid: 0000-0003-0370-9835 - first_name: Andreas full_name: Rappold, Andreas last_name: Rappold - first_name: Werner full_name: Müller, Werner last_name: Müller citation: ama: Perrone E, Rappold A, Müller W. D inf s optimality in copula models. Statistical Methods and Applications. 2017;26(3):403-418. doi:10.1007/s10260-016-0375-6 apa: Perrone, E., Rappold, A., & Müller, W. (2017). D inf s optimality in copula models. Statistical Methods and Applications. Springer. https://doi.org/10.1007/s10260-016-0375-6 chicago: Perrone, Elisa, Andreas Rappold, and Werner Müller. “D Inf s Optimality in Copula Models.” Statistical Methods and Applications. Springer, 2017. https://doi.org/10.1007/s10260-016-0375-6. ieee: E. Perrone, A. Rappold, and W. Müller, “D inf s optimality in copula models,” Statistical Methods and Applications, vol. 26, no. 3. Springer, pp. 403–418, 2017. ista: Perrone E, Rappold A, Müller W. 2017. D inf s optimality in copula models. Statistical Methods and Applications. 26(3), 403–418. mla: Perrone, Elisa, et al. “D Inf s Optimality in Copula Models.” Statistical Methods and Applications, vol. 26, no. 3, Springer, 2017, pp. 403–18, doi:10.1007/s10260-016-0375-6. short: E. Perrone, A. Rappold, W. Müller, Statistical Methods and Applications 26 (2017) 403–418. date_created: 2018-12-11T11:50:31Z date_published: 2017-08-01T00:00:00Z date_updated: 2023-09-20T11:25:09Z day: '01' ddc: - '519' department: - _id: CaUh doi: 10.1007/s10260-016-0375-6 external_id: isi: - '000407973200004' file: - access_level: open_access checksum: 0b2d1b647ca96e9ef13a14b8b6775e0f content_type: application/pdf creator: system date_created: 2018-12-12T10:16:13Z date_updated: 2020-07-14T12:44:37Z file_id: '5199' file_name: IST-2017-739-v1+2_10260_2016_375_MOESM1_ESM.pdf file_size: 56664 relation: main_file - access_level: open_access checksum: 3321ef34e02e28acfc427f77cf32812a content_type: application/pdf creator: system date_created: 2018-12-12T10:16:14Z date_updated: 2020-07-14T12:44:37Z file_id: '5200' file_name: IST-2017-739-v1+3_s10260-016-0375-6.pdf file_size: 688953 relation: main_file file_date_updated: 2020-07-14T12:44:37Z has_accepted_license: '1' intvolume: ' 26' isi: 1 issue: '3' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 403 - 418 publication: Statistical Methods and Applications publication_status: published publisher: Springer publist_id: '6189' pubrep_id: '739' quality_controlled: '1' scopus_import: '1' status: public title: D inf s optimality in copula models tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 26 year: '2017' ... --- _id: '1089' abstract: - lang: eng text: We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional semigraphoid which is upward-stable and singleton-transitive. In addition, we prove that any MTP2 distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP2 distributions and discuss ways of constructing MTP2 distributions; in particular we give conditions on the log-linear parameters of a discrete distribution which ensure MTP2 and characterize conditional Gaussian distributions which satisfy MTP2. article_processing_charge: No author: - first_name: Shaun full_name: Fallat, Shaun last_name: Fallat - first_name: Steffen full_name: Lauritzen, Steffen last_name: Lauritzen - first_name: Kayvan full_name: Sadeghi, Kayvan last_name: Sadeghi - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Nanny full_name: Wermuth, Nanny last_name: Wermuth - first_name: Piotr full_name: Zwiernik, Piotr last_name: Zwiernik citation: ama: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. Total positivity in Markov structures. Annals of Statistics. 2017;45(3):1152-1184. doi:10.1214/16-AOS1478 apa: Fallat, S., Lauritzen, S., Sadeghi, K., Uhler, C., Wermuth, N., & Zwiernik, P. (2017). Total positivity in Markov structures. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AOS1478 chicago: Fallat, Shaun, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny Wermuth, and Piotr Zwiernik. “Total Positivity in Markov Structures.” Annals of Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AOS1478. ieee: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, and P. Zwiernik, “Total positivity in Markov structures,” Annals of Statistics, vol. 45, no. 3. Institute of Mathematical Statistics, pp. 1152–1184, 2017. ista: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. 2017. Total positivity in Markov structures. Annals of Statistics. 45(3), 1152–1184. mla: Fallat, Shaun, et al. “Total Positivity in Markov Structures.” Annals of Statistics, vol. 45, no. 3, Institute of Mathematical Statistics, 2017, pp. 1152–84, doi:10.1214/16-AOS1478. short: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, P. Zwiernik, Annals of Statistics 45 (2017) 1152–1184. date_created: 2018-12-11T11:50:05Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T11:46:53Z day: '01' department: - _id: CaUh doi: 10.1214/16-AOS1478 external_id: isi: - '000404395900008' intvolume: ' 45' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1510.01290 month: '06' oa: 1 oa_version: Submitted Version page: 1152 - 1184 project: - _id: 2530CA10-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Y 903-N35 name: 'Gaussian Graphical Models: Theory and Applications' publication: Annals of Statistics publication_identifier: issn: - '00905364' publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6288' quality_controlled: '1' scopus_import: '1' status: public title: Total positivity in Markov structures type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 45 year: '2017' ... --- _id: '1293' abstract: - lang: eng text: For a graph G with p vertices the closed convex cone S⪰0(G) consists of all real positive semidefinite p×p matrices whose sparsity pattern is given by G, that is, those matrices with zeros in the off-diagonal entries corresponding to nonedges of G. The extremal rays of this cone and their associated ranks have applications to matrix completion problems, maximum likelihood estimation in Gaussian graphical models in statistics, and Gauss elimination for sparse matrices. While the maximum rank of an extremal ray in S⪰0(G), known as the sparsity order of G, has been characterized for different classes of graphs, we here study all possible extremal ranks of S⪰0(G). We investigate when the geometry of the (±1)-cut polytope of G yields a polyhedral characterization of the set of extremal ranks of S⪰0(G). For a graph G without K5 minors, we show that appropriately chosen normal vectors to the facets of the (±1)-cut polytope of G specify the off-diagonal entries of extremal matrices in S⪰0(G). We also prove that for appropriately chosen scalars the constant term of the linear equation of each facet-supporting hyperplane is the rank of its corresponding extremal matrix in S⪰0(G). Furthermore, we show that if G is series-parallel then this gives a complete characterization of all possible extremal ranks of S⪰0(G). Consequently, the sparsity order problem for series-parallel graphs can be solved in terms of polyhedral geometry. acknowledgement: We wish to thank Alexander Engström and Bernd Sturmfels for various valuable discussions and insights. We also thank the two anonymous referees for their thoughtful feedback on the paper. CU was partially supported by the Austrian Science Fund (FWF) Y 903-N35. author: - first_name: Liam T full_name: Solus, Liam T id: 2AADA620-F248-11E8-B48F-1D18A9856A87 last_name: Solus - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Ruriko full_name: Yoshida, Ruriko last_name: Yoshida citation: ama: Solus LT, Uhler C, Yoshida R. Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors. Linear Algebra and Its Applications. 2016;509:247-275. doi:10.1016/j.laa.2016.07.026 apa: Solus, L. T., Uhler, C., & Yoshida, R. (2016). Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2016.07.026 chicago: Solus, Liam T, Caroline Uhler, and Ruriko Yoshida. “Extremal Positive Semidefinite Matrices Whose Sparsity Pattern Is given by Graphs without K5 Minors.” Linear Algebra and Its Applications. Elsevier, 2016. https://doi.org/10.1016/j.laa.2016.07.026. ieee: L. T. Solus, C. Uhler, and R. Yoshida, “Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors,” Linear Algebra and Its Applications, vol. 509. Elsevier, pp. 247–275, 2016. ista: Solus LT, Uhler C, Yoshida R. 2016. Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors. Linear Algebra and Its Applications. 509, 247–275. mla: Solus, Liam T., et al. “Extremal Positive Semidefinite Matrices Whose Sparsity Pattern Is given by Graphs without K5 Minors.” Linear Algebra and Its Applications, vol. 509, Elsevier, 2016, pp. 247–75, doi:10.1016/j.laa.2016.07.026. short: L.T. Solus, C. Uhler, R. Yoshida, Linear Algebra and Its Applications 509 (2016) 247–275. date_created: 2018-12-11T11:51:11Z date_published: 2016-11-15T00:00:00Z date_updated: 2021-01-12T06:49:40Z day: '15' department: - _id: CaUh doi: 10.1016/j.laa.2016.07.026 intvolume: ' 509' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/pdf/1506.06702.pdf month: '11' oa: 1 oa_version: Preprint page: 247 - 275 project: - _id: 2530CA10-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Y 903-N35 name: 'Gaussian Graphical Models: Theory and Applications' publication: Linear Algebra and Its Applications publication_status: published publisher: Elsevier publist_id: '6024' quality_controlled: '1' scopus_import: 1 status: public title: Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 509 year: '2016' ... --- _id: '1480' abstract: - lang: eng text: 'Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials. ' author: - first_name: Mateusz full_name: Michałek, Mateusz last_name: Michałek - first_name: Bernd full_name: Sturmfels, Bernd last_name: Sturmfels - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Piotr full_name: Zwiernik, Piotr last_name: Zwiernik citation: ama: Michałek M, Sturmfels B, Uhler C, Zwiernik P. Exponential varieties. Proceedings of the London Mathematical Society. 2016;112(1):27-56. doi:10.1112/plms/pdv066 apa: Michałek, M., Sturmfels, B., Uhler, C., & Zwiernik, P. (2016). Exponential varieties. Proceedings of the London Mathematical Society. Oxford University Press. https://doi.org/10.1112/plms/pdv066 chicago: Michałek, Mateusz, Bernd Sturmfels, Caroline Uhler, and Piotr Zwiernik. “Exponential Varieties.” Proceedings of the London Mathematical Society. Oxford University Press, 2016. https://doi.org/10.1112/plms/pdv066. ieee: M. Michałek, B. Sturmfels, C. Uhler, and P. Zwiernik, “Exponential varieties,” Proceedings of the London Mathematical Society, vol. 112, no. 1. Oxford University Press, pp. 27–56, 2016. ista: Michałek M, Sturmfels B, Uhler C, Zwiernik P. 2016. Exponential varieties. Proceedings of the London Mathematical Society. 112(1), 27–56. mla: Michałek, Mateusz, et al. “Exponential Varieties.” Proceedings of the London Mathematical Society, vol. 112, no. 1, Oxford University Press, 2016, pp. 27–56, doi:10.1112/plms/pdv066. short: M. Michałek, B. Sturmfels, C. Uhler, P. Zwiernik, Proceedings of the London Mathematical Society 112 (2016) 27–56. date_created: 2018-12-11T11:52:16Z date_published: 2016-01-07T00:00:00Z date_updated: 2021-01-12T06:51:02Z day: '07' department: - _id: CaUh doi: 10.1112/plms/pdv066 intvolume: ' 112' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1412.6185 month: '01' oa: 1 oa_version: Preprint page: 27 - 56 publication: Proceedings of the London Mathematical Society publication_status: published publisher: Oxford University Press publist_id: '5714' quality_controlled: '1' scopus_import: 1 status: public title: Exponential varieties type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 112 year: '2016' ... --- _id: '1833' abstract: - lang: eng text: 'Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in the table, and not necessarily containing the overall effect, that is, a common parameter in every cell. Similarly to log-linear models, relational models can be extended to non-negative distributions, but the extension requires more complex methods. An extended relational model is defined as an algebraic variety, and it turns out to be the closure of the original model with respect to the Bregman divergence. In the extended relational model, the MLE of the cell parameters always exists and is unique, but some of its properties may be different from those of the MLE under log-linear models. The MLE can be computed using a generalized iterative scaling procedure based on Bregman projections. ' 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. On the closure of relational models. Journal of Multivariate Analysis. 2016;143:440-452. doi:10.1016/j.jmva.2015.10.005 apa: Klimova, A., & Rudas, T. (2016). On the closure of relational models. Journal of Multivariate Analysis. Elsevier. https://doi.org/10.1016/j.jmva.2015.10.005 chicago: Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” Journal of Multivariate Analysis. Elsevier, 2016. https://doi.org/10.1016/j.jmva.2015.10.005. ieee: A. Klimova and T. Rudas, “On the closure of relational models,” Journal of Multivariate Analysis, vol. 143. Elsevier, pp. 440–452, 2016. ista: Klimova A, Rudas T. 2016. On the closure of relational models. Journal of Multivariate Analysis. 143, 440–452. mla: Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” Journal of Multivariate Analysis, vol. 143, Elsevier, 2016, pp. 440–52, doi:10.1016/j.jmva.2015.10.005. short: A. Klimova, T. Rudas, Journal of Multivariate Analysis 143 (2016) 440–452. date_created: 2018-12-11T11:54:15Z date_published: 2016-01-01T00:00:00Z date_updated: 2021-01-12T06:53:30Z day: '01' department: - _id: CaUh doi: 10.1016/j.jmva.2015.10.005 intvolume: ' 143' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1501.00600 month: '01' oa: 1 oa_version: Preprint page: 440 - 452 publication: Journal of Multivariate Analysis publication_status: published publisher: Elsevier publist_id: '5270' quality_controlled: '1' scopus_import: 1 status: public title: On the closure of relational models type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 143 year: '2016' ... --- _id: '1547' abstract: - lang: eng text: Let G be a graph on the vertex set V(G) = {x1,…,xn} with the edge set E(G), and let R = K[x1,…, xn] be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials xixj with {xi,xj} ∈ E(G), and the vertex cover ideal IG generated by monomials ∏xi∈Cxi for all minimal vertex covers C of G. A minimal vertex cover of G is a subset C ⊂ V(G) such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers LG and we explicitly describe the minimal free resolution of the ideal associated to LG which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice. author: - first_name: Fatemeh full_name: Mohammadi, Fatemeh id: 2C29581E-F248-11E8-B48F-1D18A9856A87 last_name: Mohammadi - first_name: Somayeh full_name: Moradi, Somayeh last_name: Moradi citation: ama: Mohammadi F, Moradi S. Resolution of unmixed bipartite graphs. Bulletin of the Korean Mathematical Society. 2015;52(3):977-986. doi:10.4134/BKMS.2015.52.3.977 apa: Mohammadi, F., & Moradi, S. (2015). Resolution of unmixed bipartite graphs. Bulletin of the Korean Mathematical Society. Korean Mathematical Society. https://doi.org/10.4134/BKMS.2015.52.3.977 chicago: Mohammadi, Fatemeh, and Somayeh Moradi. “Resolution of Unmixed Bipartite Graphs.” Bulletin of the Korean Mathematical Society. Korean Mathematical Society, 2015. https://doi.org/10.4134/BKMS.2015.52.3.977. ieee: F. Mohammadi and S. Moradi, “Resolution of unmixed bipartite graphs,” Bulletin of the Korean Mathematical Society, vol. 52, no. 3. Korean Mathematical Society, pp. 977–986, 2015. ista: Mohammadi F, Moradi S. 2015. Resolution of unmixed bipartite graphs. Bulletin of the Korean Mathematical Society. 52(3), 977–986. mla: Mohammadi, Fatemeh, and Somayeh Moradi. “Resolution of Unmixed Bipartite Graphs.” Bulletin of the Korean Mathematical Society, vol. 52, no. 3, Korean Mathematical Society, 2015, pp. 977–86, doi:10.4134/BKMS.2015.52.3.977. short: F. Mohammadi, S. Moradi, Bulletin of the Korean Mathematical Society 52 (2015) 977–986. date_created: 2018-12-11T11:52:39Z date_published: 2015-05-31T00:00:00Z date_updated: 2021-01-12T06:51:31Z day: '31' department: - _id: CaUh doi: 10.4134/BKMS.2015.52.3.977 intvolume: ' 52' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/0901.3015 month: '05' oa: 1 oa_version: Preprint page: 977 - 986 publication: Bulletin of the Korean Mathematical Society publication_identifier: eissn: - 2234-3016 publication_status: published publisher: Korean Mathematical Society publist_id: '5624' quality_controlled: '1' scopus_import: 1 status: public title: Resolution of unmixed bipartite graphs type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 52 year: '2015' ... --- _id: '1579' abstract: - lang: eng text: We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. This constitutes the largest family of enumerative problems whose Galois groups have been largely determined. Using a criterion of Vakil and a special position argument due to Schubert, our result follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, a combinatorial injection proves the inequality. For the remaining cases, we use the Weyl integral formulas to obtain an integral formula for these Kostka numbers. This rewrites the inequality as an integral, which we estimate to establish the inequality. acknowledgement: "This research was supported in part by NSF grant DMS-915211 and the Institut Mittag-Leffler.\r\n" article_processing_charge: No author: - first_name: Christopher full_name: Brooks, Christopher last_name: Brooks - 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 citation: ama: Brooks C, Martin del Campo Sanchez A, Sottile F. Galois groups of Schubert problems of lines are at least alternating. Transactions of the American Mathematical Society. 2015;367(6):4183-4206. doi:10.1090/S0002-9947-2014-06192-8 apa: Brooks, C., Martin del Campo Sanchez, A., & Sottile, F. (2015). Galois groups of Schubert problems of lines are at least alternating. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/S0002-9947-2014-06192-8 chicago: Brooks, Christopher, Abraham Martin del Campo Sanchez, and Frank Sottile. “Galois Groups of Schubert Problems of Lines Are at Least Alternating.” Transactions of the American Mathematical Society. American Mathematical Society, 2015. https://doi.org/10.1090/S0002-9947-2014-06192-8. ieee: C. Brooks, A. Martin del Campo Sanchez, and F. Sottile, “Galois groups of Schubert problems of lines are at least alternating,” Transactions of the American Mathematical Society, vol. 367, no. 6. American Mathematical Society, pp. 4183–4206, 2015. ista: Brooks C, Martin del Campo Sanchez A, Sottile F. 2015. Galois groups of Schubert problems of lines are at least alternating. Transactions of the American Mathematical Society. 367(6), 4183–4206. mla: Brooks, Christopher, et al. “Galois Groups of Schubert Problems of Lines Are at Least Alternating.” Transactions of the American Mathematical Society, vol. 367, no. 6, American Mathematical Society, 2015, pp. 4183–206, doi:10.1090/S0002-9947-2014-06192-8. short: C. Brooks, A. Martin del Campo Sanchez, F. Sottile, Transactions of the American Mathematical Society 367 (2015) 4183–4206. date_created: 2018-12-11T11:52:50Z date_published: 2015-06-01T00:00:00Z date_updated: 2021-01-12T06:51:43Z day: '01' department: - _id: CaUh doi: 10.1090/S0002-9947-2014-06192-8 intvolume: ' 367' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1207.4280 month: '06' oa: 1 oa_version: Preprint page: 4183 - 4206 publication: Transactions of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5592' quality_controlled: '1' scopus_import: 1 status: public title: Galois groups of Schubert problems of lines are at least alternating type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 367 year: '2015' ... --- _id: '1997' abstract: - lang: eng text: We prove that the three-state toric homogeneous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals is generated by quadratic binomials. This was conjectured by Haws, Martin del Campo, Takemura and Yoshida, who proved that they are generated by degree six binomials. author: - first_name: Patrik full_name: Noren, Patrik id: 46870C74-F248-11E8-B48F-1D18A9856A87 last_name: Noren citation: ama: Noren P. The three-state toric homogeneous Markov chain model has Markov degree two. Journal of Symbolic Computation. 2015;68/Part 2(May-June):285-296. doi:10.1016/j.jsc.2014.09.014 apa: Noren, P. (2015). The three-state toric homogeneous Markov chain model has Markov degree two. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/j.jsc.2014.09.014 chicago: Noren, Patrik. “The Three-State Toric Homogeneous Markov Chain Model Has Markov Degree Two.” Journal of Symbolic Computation. Elsevier, 2015. https://doi.org/10.1016/j.jsc.2014.09.014. ieee: P. Noren, “The three-state toric homogeneous Markov chain model has Markov degree two,” Journal of Symbolic Computation, vol. 68/Part 2, no. May-June. Elsevier, pp. 285–296, 2015. ista: Noren P. 2015. The three-state toric homogeneous Markov chain model has Markov degree two. Journal of Symbolic Computation. 68/Part 2(May-June), 285–296. mla: Noren, Patrik. “The Three-State Toric Homogeneous Markov Chain Model Has Markov Degree Two.” Journal of Symbolic Computation, vol. 68/Part 2, no. May-June, Elsevier, 2015, pp. 285–96, doi:10.1016/j.jsc.2014.09.014. short: P. Noren, Journal of Symbolic Computation 68/Part 2 (2015) 285–296. date_created: 2018-12-11T11:55:07Z date_published: 2015-05-01T00:00:00Z date_updated: 2021-01-12T06:54:35Z day: '01' department: - _id: CaUh doi: 10.1016/j.jsc.2014.09.014 issue: May-June language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1207.0077 month: '05' oa: 1 oa_version: Preprint page: 285 - 296 publication: Journal of Symbolic Computation publication_status: published publisher: Elsevier publist_id: '5082' quality_controlled: '1' scopus_import: 1 status: public title: The three-state toric homogeneous Markov chain model has Markov degree two type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 68/Part 2 year: '2015' ... --- _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' ... --- _id: '2007' abstract: - lang: eng text: Maximum likelihood estimation under relational models, with or without the overall effect. For more information see the reference manual article_processing_charge: No 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. gIPFrm: Generalized iterative proportional fitting for relational models. 2014.' apa: 'Klimova, A., & Rudas, T. (2014). gIPFrm: Generalized iterative proportional fitting for relational models. The Comprehensive R Archive Network.' chicago: 'Klimova, Anna, and Tamás Rudas. “GIPFrm: Generalized Iterative Proportional Fitting for Relational Models.” The Comprehensive R Archive Network, 2014.' ieee: 'A. Klimova and T. Rudas, “gIPFrm: Generalized iterative proportional fitting for relational models.” The Comprehensive R Archive Network, 2014.' ista: 'Klimova A, Rudas T. 2014. gIPFrm: Generalized iterative proportional fitting for relational models, The Comprehensive R Archive Network.' 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). date_created: 2018-12-11T11:55:10Z date_published: 2014-03-20T00:00:00Z date_updated: 2022-08-26T08:12:12Z day: '20' department: - _id: CaUh main_file_link: - open_access: '1' url: 'https://CRAN.R-project.org/package=gIPFrm ' month: '03' oa: 1 oa_version: Published Version publisher: The Comprehensive R Archive Network publist_id: '5069' status: public title: 'gIPFrm: Generalized iterative proportional fitting for relational models' type: research_data_reference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2013' 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" 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). author: - first_name: Shaowei full_name: Lin, Shaowei last_name: Lin - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 - first_name: Bernd full_name: Sturmfels, Bernd last_name: Sturmfels - first_name: Peter full_name: Bühlmann, Peter last_name: Bühlmann 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 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. 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. 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. short: S. Lin, C. Uhler, B. Sturmfels, P. Bühlmann, Foundations of Computational Mathematics 14 (2014) 1079–1116. date_created: 2018-12-11T11:55:12Z date_published: 2014-10-10T00:00:00Z date_updated: 2021-01-12T06:54:43Z day: '10' department: - _id: CaUh doi: 10.1007/s10208-014-9205-0 intvolume: ' 14' issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1209.0285 month: '10' oa: 1 oa_version: Submitted Version page: 1079 - 1116 publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '5063' quality_controlled: '1' scopus_import: 1 status: public title: Hypersurfaces and their singularities in partial correlation testing type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2014' ... --- _id: '2047' abstract: - lang: eng 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. acknowledgement: This research was partially supported by BCS- 0941518 to the Department of Statistics at Carnegie Mellon University. alternative_title: - LNCS author: - first_name: Fei full_name: Yu, Fei last_name: Yu - first_name: Michal full_name: Rybar, Michal id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87 last_name: Rybar - 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: Fienberg, Stephen last_name: Fienberg citation: 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' 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' 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. 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. 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.' 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. conference: end_date: 2014-09-19 location: Ibiza, Spain name: 'PSD: Privacy in Statistical Databases' start_date: 2014-09-17 date_created: 2018-12-11T11:55:24Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T06:54:57Z day: '01' department: - _id: KrPi - _id: CaUh doi: 10.1007/978-3-319-11257-2_14 editor: - first_name: Josep full_name: Domingo Ferrer, Josep last_name: Domingo Ferrer external_id: arxiv: - '1407.8067' intvolume: ' 8744' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1407.8067 month: '01' oa: 1 oa_version: Submitted Version page: 170 - 184 project: - _id: 25636330-B435-11E9-9278-68D0E5697425 grant_number: 11-NSF-1070 name: ROOTS Genome-wide Analysis of Root Traits publication: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) publication_status: published publisher: Springer publist_id: '5004' quality_controlled: '1' scopus_import: 1 status: public title: Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8744 year: '2014' ... --- _id: '2178' abstract: - lang: eng 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. acknowledgement: Research of Martín del Campo supported in part by NSF Grant DMS-915211. author: - first_name: David full_name: Haws, David last_name: Haws - first_name: Abraham full_name: Martin Del Campo Sanchez, Abraham id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87 last_name: Martin Del Campo Sanchez - first_name: Akimichi full_name: Takemura, Akimichi last_name: Takemura - first_name: Ruriko full_name: Yoshida, Ruriko last_name: Yoshida citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:56:10Z date_published: 2014-03-01T00:00:00Z date_updated: 2021-01-12T06:55:48Z day: '01' department: - _id: CaUh doi: 10.1007/s13366-013-0178-y intvolume: ' 55' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1204.3070 month: '03' oa: 1 oa_version: Submitted Version page: 161 - 188 publication: Beitrage zur Algebra und Geometrie publication_status: published publisher: Springer publist_id: '4804' quality_controlled: '1' scopus_import: 1 status: public title: Markov degree of the three-state toric homogeneous Markov chain model type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2014' ... --- _id: '2012' 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. 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 article_number: '1401.0468' article_processing_charge: No author: - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham - first_name: Michael full_name: Kerber, Michael last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 citation: ama: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/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 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. ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. . ista: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. 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.). date_created: 2018-12-11T11:55:12Z date_published: 2014-01-01T00:00:00Z date_updated: 2023-10-18T08:06:45Z day: '01' department: - _id: HeEd - _id: CaUh doi: 10.48550/arXiv.1401.0468 external_id: arxiv: - '1401.0468' language: - iso: eng main_file_link: - open_access: '1' url: http://cccg.ca/proceedings/2014/papers/paper23.pdf month: '01' oa: 1 oa_version: Submitted Version publication: arXiv publication_status: submitted publist_id: '5064' status: public title: Sphere packing with limited overlap type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _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. 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: '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: '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. 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' ...