@misc{2007, abstract = {Maximum likelihood estimation under relational models, with or without the overall effect. For more information see the reference manual}, author = {Klimova, Anna and Rudas, Tamás}, publisher = {The Comprehensive R Archive Network}, title = {{gIPFrm: Generalized iterative proportional fitting for relational models}}, year = {2014}, } @article{2013, abstract = {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. }, author = {Lin, Shaowei and Uhler, Caroline and Sturmfels, Bernd and Bühlmann, Peter}, journal = {Foundations of Computational Mathematics}, number = {5}, pages = {1079 -- 1116}, publisher = {Springer}, title = {{Hypersurfaces and their singularities in partial correlation testing}}, doi = {10.1007/s10208-014-9205-0}, volume = {14}, year = {2014}, } @inproceedings{2047, abstract = {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.}, author = {Yu, Fei and Rybar, Michal and Uhler, Caroline and Fienberg, Stephen}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, editor = {Domingo Ferrer, Josep}, location = {Ibiza, Spain}, pages = {170 -- 184}, publisher = {Springer}, title = {{Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases}}, doi = {10.1007/978-3-319-11257-2_14}, volume = {8744}, year = {2014}, } @article{2178, abstract = {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.}, author = {Haws, David and Martin Del Campo Sanchez, Abraham and Takemura, Akimichi and Yoshida, Ruriko}, journal = {Beitrage zur Algebra und Geometrie}, number = {1}, pages = {161 -- 188}, publisher = {Springer}, title = {{Markov degree of the three-state toric homogeneous Markov chain model}}, doi = {10.1007/s13366-013-0178-y}, volume = {55}, year = {2014}, } @unpublished{2012, abstract = {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.}, author = {Iglesias Ham, Mabel and Kerber, Michael and Uhler, Caroline}, booktitle = {arXiv}, title = {{Sphere packing with limited overlap}}, doi = {10.48550/arXiv.1401.0468}, year = {2014}, }