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# Differentiable TAN Structure Learning for Bayesian Network Classifiers

*Proceedings of the 10th International Conference on Probabilistic Graphical Models*, PMLR 138:389-400, 2020.

#### Abstract

Learning the structure of Bayesian networks is a
difficult combinatorial optimization problem. In this paper, we consider
learning of tree-augmented naive Bayes (TAN) structures for Bayesian
network classifiers with discrete input features. Instead of performing
a combinatorial optimization over the space of possible graph
structures, the proposed method learns a distribution over graph
structures. After training, we select the most probable structure of
this distribution. This allows for a joint training of the Bayesian
network parameters along with its TAN structure using gradient-based
optimization. The proposed method is agnostic to the specific loss and
only requires that it is differentiable. We perform extensive
experiments using a hybrid generative-discriminative loss based on the
discriminative probabilistic margin. Our method consistently outperforms
random TAN structures and Chow-Liu TAN structures.