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TitleAn implicitization challenge for binary factor analysis
Author(s) María Angélica Cueto, Enrique A. Tobis, Jie-Tai Yu
TypeArticle in Journal
AbstractWe 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.
KeywordsFactor analysis, Tropical geometry, Hadamard products, Newton polytope
URL http://www.sciencedirect.com/science/article/pii/S074771711000091X
JournalJournal of Symbolic Computation
Pages1296 - 1315
Translation No
Refereed No