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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2010
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_07477171_v45_n12_p1296_Cueto |
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paperaa:paper_07477171_v45_n12_p1296_Cueto2023-06-12T16:48:13Z An implicitization challenge for binary factor analysis J. Symb. Comput. 2010;45(12):1296-1315 Cueto, M.A. Tobis, E.A. Yu, J. Factor analysis Hadamard products Newton polytope Tropical geometry 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. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v45_n12_p1296_Cueto |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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 |
| work_keys_str_mv |
AT cuetoma animplicitizationchallengeforbinaryfactoranalysis AT tobisea animplicitizationchallengeforbinaryfactoranalysis AT yuj animplicitizationchallengeforbinaryfactoranalysis AT cuetoma implicitizationchallengeforbinaryfactoranalysis AT tobisea implicitizationchallengeforbinaryfactoranalysis AT yuj implicitizationchallengeforbinaryfactoranalysis |
| _version_ |
1769810033590140928 |