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Concise representations and construction algorithms for semi-graphoid independency models

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Abstract
The conditional independencies from a joint probability distribution constitute a model which is closed under the semi-graphoid properties of independency. These models typically are exponentially large in size and cannot be feasibly enumerated. For describing a semi-graphoid model therefore, researchers have proposed a more concise representation. This representation is composed of a representative subset of the independencies involved, called a basis, and lets all other independencies be implicitly defined by the semi-graphoid properties. An algorithm is available for computing such a basis for a semi-graphoid independency model. In this paper, we identify some new properties of a basis in general which can be exploited for arriving at an even more concise representation of a semi- graphoid model. Based upon these properties, we present an enhanced algorithm for basis construction which never returns a larger basis for a given independency model than currently existing algorithms.
Keywords
Conditional independence, Semi-graphoid axioms, Closure, Closure representation, Dominant independence statements

Citation

Please use this url to cite or link to this publication:

Chicago
Lopatatzidis, Stavros, and Linda C. van der Gaag. 2017. “Concise Representations and Construction Algorithms for Semi-graphoid Independency Models.” International Journal of Approximate Reasoning.
APA
Lopatatzidis, S., & van der Gaag, L. C. (2017). Concise representations and construction algorithms for semi-graphoid independency models. International Journal of Approximate Reasoning.
Vancouver
1.
Lopatatzidis S, van der Gaag LC. Concise representations and construction algorithms for semi-graphoid independency models. International Journal of Approximate Reasoning. 2017;
MLA
Lopatatzidis, Stavros, and Linda C. van der Gaag. “Concise Representations and Construction Algorithms for Semi-graphoid Independency Models.” International Journal of Approximate Reasoning (2017): n. pag. Print.
@article{8081470,
  abstract     = {The conditional independencies from a joint probability distribution constitute a model which is closed under the semi-graphoid properties of independency. These models typically are exponentially large in size and cannot be feasibly enumerated. For describing a semi-graphoid model therefore, researchers have proposed a more concise representation. This representation is composed of a representative subset of the independencies involved, called a basis, and lets all other independencies be implicitly defined by the semi-graphoid properties. An algorithm is available for computing such a basis for a semi-graphoid independency model. In this paper, we identify some new properties of a basis in general which can be exploited for arriving at an even more concise representation of a semi- graphoid model. Based upon these properties, we present an enhanced algorithm for basis construction which never returns a larger basis for a given independency model than currently existing algorithms.},
  author       = {Lopatatzidis, Stavros and van der Gaag, Linda C.},
  journal      = {International Journal of Approximate Reasoning},
  keyword      = {Conditional independence,Semi-graphoid axioms,Closure,Closure representation,Dominant independence statements},
  language     = {eng},
  title        = {Concise representations and construction algorithms for semi-graphoid independency models},
  year         = {2017},
}