Details:
Title  An implicitization challenge for binary factor analysis  Author(s)  María Angélica Cueto, Enrique A. Tobis, JieTai Yu  Type  Article in Journal  Abstract  We use tropical geometry to compute the multidegree and Newton polytope of the hypersurface of a statistical model with two hidden and four observed binary random variables, solving an open question stated by Drton, Sturmfels and Sullivant in (Drton et al., 2009, Ch. VI, Problem 7.7). The model is obtained from the undirected graphical model of the complete bipartite graph K 2 , 4 by marginalizing two of the six binary random variables. We present algorithms for computing the Newton polytope of its defining equation by parallel walks along the polytope and its normal fan. In this way we compute vertices of the polytope. Finally, we also compute and certify its facets by studying tangent cones of the polytope at the symmetry classes of vertices. The Newton polytope has 17 214 912 vertices in 44 938 symmetry classes and 70 646 facets in 246 symmetry classes.  Keywords  Factor analysis, Tropical geometry, Hadamard products, Newton polytope  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771711000091X 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  12  Pages  1296  1315  Year  2010  Note  MEGA’2009  Edition  0  Translation 
No  Refereed 
No 
