Learning tree-augmented naive Bayesian network by reduced space requirements

The tree-augmented naive Bayesian network (TAN) based on the Bayes theorem is a restricted Bayesian network. Its classification performance is superior to naive Bayes, and its time complexity is much lower than general Bayesian networks. So TAN embodies a good trade-off between the quality of approximation correlation among attributes and the computational complexity in the learning stage. However, its memory requirement is quadratic in the number of attributes, which restricts its application in high dimensional data. This paper proposes a new algorithm for constructing TAN, and proves the correctness of this algorithm. The space complexity of this new algorithm is linear in the number of attributes.