Statistical independence from the viewpoint of linear algebra

Authors:
Shusaku Tsumoto
Affiliations:
Department of Medical Informatics, Shimane University, School of Medicine, Japan
Venue:
ISMIS'05 Proceedings of the 15th international conference on Foundations of Intelligent Systems
Year:
2005

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Abstract

A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other with the information on a partition of universe generated by these attributes. Thus, this table can be viewed as a relation between two attributes with respect to information granularity. This paper focuses on statistical independence in a contingency table from the viewpoint of granular computing, which shows that statistical independence in a contingency table is a special form of linear dependence. The discussions also show that when a contingency table is viewed as a matrix, its rank is equal to 1.0. Thus, the degree of independence, rank plays a very important role in extracting a probabilistic model from a given contingency table.