An implicitization challenge for binary factor analysis
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 o...
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I28-R145-paper_07477171_v45_n12_p1296_Cueto_oai2024-08-16 Cueto, M.A. Tobis, E.A. Yu, J. 2010 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. © 2010. Fil:Tobis, E.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_07477171_v45_n12_p1296_Cueto info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Symb. Comput. 2010;45(12):1296-1315 Factor analysis Hadamard products Newton polytope Tropical geometry An implicitization challenge for binary factor analysis info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v45_n12_p1296_Cueto_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| topic |
Factor analysis Hadamard products Newton polytope Tropical geometry |
| spellingShingle |
Factor analysis Hadamard products Newton polytope Tropical geometry Cueto, M.A. Tobis, E.A. Yu, J. An implicitization challenge for binary factor analysis |
| topic_facet |
Factor analysis Hadamard products Newton polytope Tropical geometry |
| description |
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. © 2010. |
| format |
Artículo Artículo publishedVersion |
| author |
Cueto, M.A. Tobis, E.A. Yu, J. |
| author_facet |
Cueto, M.A. Tobis, E.A. Yu, J. |
| author_sort |
Cueto, M.A. |
| title |
An implicitization challenge for binary factor analysis |
| title_short |
An implicitization challenge for binary factor analysis |
| title_full |
An implicitization challenge for binary factor analysis |
| title_fullStr |
An implicitization challenge for binary factor analysis |
| title_full_unstemmed |
An implicitization challenge for binary factor analysis |
| title_sort |
implicitization challenge for binary factor analysis |
| publishDate |
2010 |
| url |
http://hdl.handle.net/20.500.12110/paper_07477171_v45_n12_p1296_Cueto https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v45_n12_p1296_Cueto_oai |
| work_keys_str_mv |
AT cuetoma animplicitizationchallengeforbinaryfactoranalysis AT tobisea animplicitizationchallengeforbinaryfactoranalysis AT yuj animplicitizationchallengeforbinaryfactoranalysis AT cuetoma implicitizationchallengeforbinaryfactoranalysis AT tobisea implicitizationchallengeforbinaryfactoranalysis AT yuj implicitizationchallengeforbinaryfactoranalysis |
| _version_ |
1809356912202874880 |