The statistical analysis of compositional data
The statistical analysis of compositional data
On the Optimality of the Simple Bayesian Classifier under Zero-One Loss
Machine Learning - Special issue on learning with probabilistic representations
Generalized Dirichlet distribution in Bayesian analysis
Applied Mathematics and Computation
Machine Learning
On Estimating Probabilities in Tree Pruning
EWSL '91 Proceedings of the European Working Session on Machine Learning
Statistics for Business and Economics (with Student CD-ROM, iPod Key Term, and InfoTrac )
Statistics for Business and Economics (with Student CD-ROM, iPod Key Term, and InfoTrac )
Computational Statistics & Data Analysis
Individual attribute prior setting methods for naïve Bayesian classifiers
Pattern Recognition
Infinite Liouville mixture models with application to text and texture categorization
Pattern Recognition Letters
A hybrid discretization method for naïve Bayesian classifiers
Pattern Recognition
Data Mining and Knowledge Discovery
Naïve Bayesian Classifiers with Multinomial Models for rRNA Taxonomic Assignment
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The prior distribution of an attribute in a naïve Bayesian classifier is typically assumed to be a Dirichlet distribution, and this is called the Dirichlet assumption. The variables in a Dirichlet random vector can never be positively correlated and must have the same confidence level as measured by normalized variance. Both the generalized Dirichlet and the Liouville distributions include the Dirichlet distribution as a special case. These two multivariate distributions, also defined on the unit simplex, are employed to investigate the impact of the Dirichlet assumption in naïve Bayesian classifiers. We propose methods to construct appropriate generalized Dirichlet and Liouville priors for naïve Bayesian classifiers. Our experimental results on 18 data sets reveal that the generalized Dirichlet distribution has the best performance among the three distribution families. Not only is the Dirichlet assumption inappropriate, but also forcing the variables in a prior to be all positively correlated can deteriorate the performance of the naïve Bayesian classifier.