دورية أكاديمية
Chordal graphs to identify graphical model solutions of maximum of entropy under constraints on marginals
| العنوان: | Chordal graphs to identify graphical model solutions of maximum of entropy under constraints on marginals |
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| المؤلفون: | Franc, Alain, Goulard, Michel, Peyrard, Nathalie |
| المساهمون: | Biodiversité, Gènes & Communautés (BioGeCo), Institut National de la Recherche Agronomique (INRA)-Université de Bordeaux (UB), Dynamiques Forestières dans l'Espace Rural (DYNAFOR), Institut National de la Recherche Agronomique (INRA)-École nationale supérieure agronomique de Toulouse ENSAT -Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Unité de Biométrie et Intelligence Artificielle (UBIA), Institut National de la Recherche Agronomique (INRA) |
| المصدر: | ISSN: 0895-4801 ; SIAM Journal on Discrete Mathematics ; https://hal.inrae.fr/hal-02653211Test ; SIAM Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2010, 24 (3), pp.1104-1116. ⟨10.1137/080736466⟩. |
| بيانات النشر: | HAL CCSD Society for Industrial and Applied Mathematics |
| سنة النشر: | 2010 |
| المجموعة: | Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
| مصطلحات موضوعية: | MAXIMUM ENTROPY, GRAPHICAL MODELS, CHORDAL GRAPHS, GRAPHE CORDAL, GRAPHE TRIANGULE, ENTROPIE MAXIMALE, EXPOSANT CANONIQUE, [SDV]Life Sciences [q-bio], [SHS]Humanities and Social Sciences, [MATH]Mathematics [math], [INFO]Computer Science [cs] |
| الوصف: | International audience ; We consider the problem of specifying the joint distribution of a collection of variables with maximum entropy when a set of marginals are fixed. One can easily derive that the structure of the solution joint distribution is that of a graphical model. The potential functions are then marginals at some power. We address the following question, Under which conditions on the set of constraints is it possible to fully identify the canonical exponents in the maximum entropy solution as functions of the problem structure? Literature related to this topic is somewhat scattered in disciplines such as statistical mechanics, information theory, graph theory, and inference in graphical models. In this article we gather and link results from these different fields. From this, we show that for a particular class of constraints set on marginals, the chordal maximal coherent sets of constraints, it is possible to derive the canonical exponents of the graphical model solution of the maximum entropy problem as the numbers of occurrences of separators in an associated join tree. Conversely, we present sufficient conditions to ensure that a graphical model is a solution of a maximum entropy problem. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | hal-02653211; https://hal.inrae.fr/hal-02653211Test; PRODINRA: 40140; WOS: 000282291600027 |
| DOI: | 10.1137/080736466 |
| الإتاحة: | https://doi.org/10.1137/080736466Test https://hal.inrae.fr/hal-02653211Test |
| رقم الانضمام: | edsbas.D2A721EB |
| قاعدة البيانات: | BASE |
| DOI: | 10.1137/080736466 |
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