TAN-FGBMLE: Tree-Augmented Naive Bayes Structure Learning Based on Fast Generative Bootstrap Maximum Likelihood Estimation for Continuous-Variable Classification

Tree-Augmented Naive Bayes (TAN) is an interpretable graphical structure model. However, its structure learning for continuous attributes depends on the class-conditional mutual information, which is sensitive to one-dimensional or two-dimensional density estimation. Accurate estimation is challenging under complex distributions such as multi-peak, long-tailed and heteroscedastic cases. To address this issue, we propose a structure learning method for TAN based on Fast Generative Bootstrap Maximum Likelihood Estimation (TAN-FGBMLE). FGBMLE consists of two stages of work. In the first stage, resampling weights and random noise are input into a network generator to rapidly produce candidate parameters, efficiently covering the latent density space without repeated independent optimization. In the second stage, optimal mixture weights are estimated by maximum likelihood estimation, assigning appropriate contributions to each candidate component. This design enables fast and accurate complex density estimation for both single and joint attributes, providing reliable computation of class-conditional mutual information. The TAN structure is then constructed using Prim’s maximum spanning tree algorithm. Experiments show that our estimation method attains higher fitting accuracy and lower runtime compared with traditional nonparametric estimators. By using open-source datasets, the TAN-FGBMLE achieves superior accuracy and recall compared to classic methods, demonstrating good robustness and interpretability. On publicly available real air quality data, it has a high classification result and produces graph structures that more accurately capture dependencies among continuous attributes.