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Naive Bayesian classification of structured data
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DOI：10.1023/B:MACH.0000039778.69032.ab.png)
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Abstract
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In this paper we present 1BC and 1BC2, two systems that perform naive Bayesian classification of structured individuals. The approach of 1BC is to project the individuals along first-order features. These features are built from the individual using structural predicates referring to related objects ( e. g., atoms within molecules), and properties applying to the individual or one or several of its related objects ( e. g., a bond between two atoms). We describe an individual in terms of elementary features consisting of zero or more structural predicates and one property; these features are treated as conditionally independent in the spirit of the naive Bayes assumption. 1BC2 represents an alternative first-order upgrade to the naive Bayesian classifier by considering probability distributions over structured objects ( e. g., a molecule as a set of atoms), and estimating those distributions from the probabilities of its elements ( which are assumed to be independent). We present a unifying view on both systems in which 1BC works in language space, and 1BC2 works in individual space. We also present a new, efficient recursive algorithm improving upon the original propositionalisation approach of 1BC. Both systems have been implemented in the context of the first-order descriptive learner Tertius, and we investigate the differences between the two systems both in computational terms and on artificially generated data. Finally, we describe a range of experiments on ILP benchmark data sets demonstrating the viability of our approach.
Keywords:
bayesian classifier
structured data
inductive logic programming
knowledge representation
first-order features
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