Estimation of logical rule quality indices based on bayesian methodology
- 1 д. т. н., проф. Нижегородского государственного технический университет им. Р. Е. Алексеева
- 2 к. т. н., проф. Нижегородского государственного технического университета им. Р. Е. Алексеева
- 3 аспирант Нижегородского государственного технического университета им. Р. Е. Алексеева
- 4 инженер ОАО «Гипрогазцентр»
Abstract
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.
How to cite
Милов В.Р., Баранов В.Г., Эпштейн А.Ю., Суслов Б.А. Оценка характеристик логических правил на основе байесовской методологии // Информационно-измерительные и управляющие системы. 2011. № 3. С. 56–61.
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