Bayesian network parameter learning using fuzzy constraints

Abstract

Prior knowledge effectively mitigates low modeling accuracy when insufficient data exist. This idea has been confirmed in many fields, especially the transformation of prior knowledge into constraints, widely employed in Bayesian network (BN) parameter learning. The role of constraints in parameter learning is the focus of this study. If parameter learning results are blindly biased toward constraints, underfitting occurs, whereas the effectiveness of the constraint intervention is weak and can not mitigate overfitting by insufficient data. Therefore, fuzzy theory is introduced in parameter learning. The fuzzy membership function is applied to measure the interference effects of constraints and improve the interpretability and accuracy of the constraint usage. For the maximum a posteriori method, hyperparameters are utilized as virtual samples to realize the intervention of parameter learning. This study proposes a fuzzy maximum a posteriori (FMAP) method, in which the hyperparameter is adjusted to a suitable value using a fuzzy membership function. For the data extension method, a proper extension function is critical to the quality of the extended data. Therefore, this paper proposes a fuzzy bootstrap (FB) method that uses a fuzzy membership function to determine the distribution of the expansion parameters. The two algorithms presented in this paper are verified on 12 standard networks. The experimental results show that the proposed methods effectively improve the accuracy of parameter learning.