TY - GEN AB - Maximum likelihood estimation under relational models, with or without the overall effect. For more information see the reference manual AU - Klimova, Anna AU - Rudas, Tamás ID - 2007 TI - gIPFrm: Generalized iterative proportional fitting for relational models ER - TY - JOUR AB - 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. AU - Lin, Shaowei AU - Uhler, Caroline AU - Sturmfels, Bernd AU - Bühlmann, Peter ID - 2013 IS - 5 JF - Foundations of Computational Mathematics TI - Hypersurfaces and their singularities in partial correlation testing VL - 14 ER - TY - CONF AB - 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. AU - Yu, Fei AU - Rybar, Michal AU - Uhler, Caroline AU - Fienberg, Stephen ED - Domingo Ferrer, Josep ID - 2047 T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) TI - Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases VL - 8744 ER - TY - JOUR AB - 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. AU - Haws, David AU - Martin Del Campo Sanchez, Abraham AU - Takemura, Akimichi AU - Yoshida, Ruriko ID - 2178 IS - 1 JF - Beitrage zur Algebra und Geometrie TI - Markov degree of the three-state toric homogeneous Markov chain model VL - 55 ER - TY - GEN AB - 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. AU - Iglesias Ham, Mabel AU - Kerber, Michael AU - Uhler, Caroline ID - 2012 T2 - arXiv TI - Sphere packing with limited overlap ER -