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Estimation of logical rule quality indices based on bayesian methodology

Keywords:

V. R. Milov, V. G. Baranov, A. Yu. Epshtein, B. A. Suslov


Regularities of a system under study can be specified in a human-understandable way via descriptive models which are frequently represented with the aid of logical rules. A rule “If R Then C” consists of a precondition R and a consequent C. For some data the statements both in the left and in the right part of the rule can be either true or false. Application of a rule to a database gives the results which may be represented via a (2×2)-matrix (a contingency table). The main characteristics of a rule: accuracy, completeness, support–are calculated based on this matrix. Strength of statistical relationship between a precondition and a consequent of the specified rule can be estimated by various means, for example, by association coefficient or contingency coefficient. The main disadvantage of these coefficients is the lack of a simple probabilistic interpretation. To estimate strength of relationship between a precondition and a consequent within the scope of probability-theoretical approach it is suggested to represent a logical rule with the aid of a Bayesian network with two discrete variables respective to a precondition R and a consequent C. A posteriori probability of the structure with the link between the variables is supposed to be the measure of statistical relationship between a precondition and a consequent. Thereby, the introduced index represents probability of existence of cause-and-effect relation between a precondition and a consequent of a logical rule depending on available data. Informativeness is considered to be another index of a logical rule and determined as the average mutual information between a precondition and a consequent. The indices introduced can be used in knowledge bases generation when building decision support systems.
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