Concise representations and construction algorithms for semi-graphoid independency models

• Published in: International journal of approximate reasoning Vol. 80; pp. 377 - 392
• Main Authors: Lopatatzidis, Stavros, van der Gaag, Linda C.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-01-2017
• Subjects: Algorithms; Closure; Closure representation; Computation; Conditional independence; Dominant independence statements; Mathematical models; Reasoning; Representations; Semi-graphoid axioms; Semi-graphoid axioms; Closure representation; Conditional independence; Closure; Dominant independence statements
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2016.06.011

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.
•Necessary conditions for excluding given independencies from basis computation.•Properties of an independency relation that help reduce the size of a representative basis.•An algorithm for basis computation that improves on earlier ones in terms of result and efficiency.