How Naive Bayes classifiers work part2(Machine Learning)
- Hierarchical Dependency Constrained Tree Augmented Naive Bayes Classifiers for Hierarchical Feature Spaces(arXiv)
Author : Cen Wan, Alex A. Freitas
Abstract : The Tree Augmented Naive Bayes (TAN) classifier is a type of probabilistic graphical model that constructs a single-parent dependency tree to estimate the distribution of the data. In this work, we propose two novel Hierarchical dependency-based Tree Augmented Naive Bayes algorithms, i.e. Hie-TAN and Hie-TAN-Lite. Both methods exploit the pre-defined parent-child (generalisation-specialisation) relationships between features as a type of constraint to learn the tree representation of dependencies among features, whilst the latter further eliminates the hierarchical redundancy during the classifier learning stage. The experimental results showed that Hie-TAN successfully obtained better predictive performance than several other hierarchical dependency constrained classification algorithms, and its predictive performance was further improved by eliminating the hierarchical redundancy, as suggested by the higher accuracy obtained by Hie-TAN-Lite.
2. Exact Learning Augmented Naive Bayes Classifier(arXiv)
Author : Shouta Sugahara, Maomi Ueno
Abstract : Earlier studies have shown that classification accuracies of Bayesian networks (BNs) obtained by maximizing the conditional log likelihood (CLL) of a class variable, given the feature variables, were higher than those obtained by maximizing the marginal likelihood (ML). However, differences between the performances of the two scores in the earlier studies may be attributed to the fact that they used approximate learning algorithms, not exact ones. This paper compares the classification accuracies of BNs with approximate learning using CLL to those with exact learning using ML. The results demonstrate that the classification accuracies of BNs obtained by maximizing the ML are higher than those obtained by maximizing the CLL for large data. However, the results also demonstrate that the classification accuracies of exact learning BNs using the ML are much worse than those of other methods when the sample size is small and the class variable has numerous parents. To resolve the problem, we propose an exact learning augmented naive Bayes classifier (ANB), which ensures a class variable with no parents. The proposed method is guaranteed to asymptotically estimate the identical class posterior to that of the exactly learned BN. Comparison experiments demonstrated the superior performance of the proposed method
