Differentiable TAN Structure Learning for Bayesian Network Classifiers
This addresses the challenge of structure learning in Bayesian networks for classification tasks, offering a differentiable approach that is incremental over existing TAN methods.
The paper tackles the combinatorial optimization problem of learning tree-augmented naive Bayes (TAN) structures for Bayesian network classifiers by proposing a method that learns a distribution over graph structures and jointly trains parameters using gradient-based optimization, resulting in consistent outperformance over random and Chow-Liu TAN structures.
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.