کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10325476 | 675388 | 2010 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An implicitization challenge for binary factor analysis
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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 K2,4 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 45, Issue 12, December 2010, Pages 1296-1315
Journal: Journal of Symbolic Computation - Volume 45, Issue 12, December 2010, Pages 1296-1315
نویسندگان
MarÃa Angélica Cueto, Enrique A. Tobis, Josephine Yu,