# Exact Learning Augmented Naive Bayes Classifier

arXiv: https://arxiv.org/abs/2107.03018 · HTML: https://mlsanity.com/paper/2107.03018/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 7 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Theory Refinement on Bayesian Networks](https://mlsanity.com/paper/1303.5709/) (2013)
- [Three Modern Roles for Logic in AI](https://mlsanity.com/paper/2004.08599/) (2020)
- [On the Relative Expressiveness of Bayesian and Neural Networks](https://mlsanity.com/paper/1812.08957/) (2018)
- [A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure Learning](https://mlsanity.com/paper/1607.04427/) (2016)
- [Advances in Bayesian Network Learning using Integer Programming](https://mlsanity.com/paper/1309.6825/) (2013)

## Abstract (arXiv)

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.