Efficient learning of decomposable models with a bounded clique size
The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theore...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/12361 |
| Acceso en línea: | http://hdl.handle.net/10810/12361 |
| Access Level: | acceso abierto |
| Palabra clave: | approximating probability distributions decomposable models bounded clique size maximum likelihood problem efficient algorithms Chow and Liu's algorithm |
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Efficient learning of decomposable models with a bounded clique sizePérez Martínez, AritzInza Cano, IñakiLozano Alonso, José Antonioapproximating probability distributionsdecomposable modelsbounded clique sizemaximum likelihood problemefficient algorithmsChow and Liu's algorithmThe learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.201420142014info:eu-repo/semantics/reportapplication/pdfhttp://hdl.handle.net/10810/12361reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésEHU-KZAA-TR;2014-07info:eu-repo/semantics/openAccessoai:addi.ehu.eus:10810/123612026-06-18T09:23:17Z |
| dc.title.none.fl_str_mv |
Efficient learning of decomposable models with a bounded clique size |
| title |
Efficient learning of decomposable models with a bounded clique size |
| spellingShingle |
Efficient learning of decomposable models with a bounded clique size Pérez Martínez, Aritz approximating probability distributions decomposable models bounded clique size maximum likelihood problem efficient algorithms Chow and Liu's algorithm |
| title_short |
Efficient learning of decomposable models with a bounded clique size |
| title_full |
Efficient learning of decomposable models with a bounded clique size |
| title_fullStr |
Efficient learning of decomposable models with a bounded clique size |
| title_full_unstemmed |
Efficient learning of decomposable models with a bounded clique size |
| title_sort |
Efficient learning of decomposable models with a bounded clique size |
| dc.creator.none.fl_str_mv |
Pérez Martínez, Aritz Inza Cano, Iñaki Lozano Alonso, José Antonio |
| author |
Pérez Martínez, Aritz |
| author_facet |
Pérez Martínez, Aritz Inza Cano, Iñaki Lozano Alonso, José Antonio |
| author_role |
author |
| author2 |
Inza Cano, Iñaki Lozano Alonso, José Antonio |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
approximating probability distributions decomposable models bounded clique size maximum likelihood problem efficient algorithms Chow and Liu's algorithm |
| topic |
approximating probability distributions decomposable models bounded clique size maximum likelihood problem efficient algorithms Chow and Liu's algorithm |
| description |
The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains. |
| publishDate |
2014 |
| dc.date.none.fl_str_mv |
2014 2014 2014 |
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info:eu-repo/semantics/report |
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report |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/10810/12361 |
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http://hdl.handle.net/10810/12361 |
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Inglés |
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Inglés |
| dc.relation.none.fl_str_mv |
EHU-KZAA-TR;2014-07 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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reponame:Addi. Archivo Digital para la Docencia y la Investigación instname:Universidad del País Vasco |
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Universidad del País Vasco |
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Addi. Archivo Digital para la Docencia y la Investigación |
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Addi. Archivo Digital para la Docencia y la Investigación |
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