Abstract
The inference of a general Bayesian network has been shown to be an NP-hard problem, even for approximate solutions. Although k-dependence Bayesian (KDB) classifier can construct at arbitrary points (values of k) along the attribute dependence spectrum, it cannot identify the changes of interdependencies when attributes take different values. Local KDB, which learns in the framework of KDB, is proposed in this study to describe the local dependencies implicated in each test instance. Based on the analysis of functional dependencies, substitution-elimination resolution, a new type of semi-naive Bayesian operation, is proposed to substitute or eliminate generalization to achieve accurate estimation of conditional probability distribution while reducing computational complexity. The final classifier, averaged k-dependence Bayesian (AKDB) classifiers, will average the output of KDB and local KDB. Experimental results on the repository of machine learning databases from the University of California Irvine (UCI) showed that AKDB has significant advantages in zero-one loss and bias relative to naive Bayes (NB), tree augmented naive Bayes (TAN), Averaged one-dependence estimators (AODE), and KDB. Moreover, KDB and local KDB show mutually complementary characteristics with respect to variance.
Highlights
Bayesian networks (BNs), which were introduced by Pearl [1], can encode dependencies among all variables
A BN can be used as a classifier that characterizes the joint distribution P (x, y)
Conditional local mutual information (CLMI) I(x; y|Z) is defined to measure the amount of information shared between two attribute values x and y when all the values of attribute Z are known, as follows: X
Summary
Bayesian networks (BNs), which were introduced by Pearl [1], can encode dependencies among all variables. Sahami [10] proposed to describe the limited dependence among variables within a general framework, which is called k-dependence Bayesian (KDB) classifier. All credible dependencies must be represented to obtain a more accurate estimation of the true joint distribution These criteria can only approximately measure the overall interdependencies between attributes, but cannot identify the change of interdependencies when attributes take different values. Substitution-elimination resolution (SER), a new type of semi-naive Bayesian operation is proposed to substitute or eliminate generalization to achieve accurate estimation of conditional probability distribution while reducing computational complexity.
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