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Bayesian network parameter learning with constraint tradeoff
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DOI：10.1016/j.ins.2025.122839.png)
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Abstract
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When training data are insufficient, purely using data to learn the Bayesian network (BN) parameters may cause overfitting, making it challenging to obtain precise parameters. Numerous studies have improved learning accuracy by translating expert knowledge into parameter constraints. However, the credibility of the constraints is difficult to ensure, and over-reliance on constraints may cause parameters to be underfitted. Therefore, this paper attempts to design a simple and effective constraint control mechanism by weighing the roles played by data and constraints in learning to balance underfitting and overfitting. The control mechanism follows two rules: the samples for each parameter have more impact on the learning accuracy than samples for the network; the more data there are, the less constraint intervention is required, and vice versa. Then, the mechanism is applied to maximum a posteriori estimation (MAP) and data extension. A constrained control mechanism MAP (CCM-MAP) is proposed. CCM-MAP quantifies prior parameters via constraints and selects hyperparameters using the mechanism. A constraint control mechanism bootstrap (CCM-B) is proposed. CCM-B quantifies prior parameters through constraints and determines the extension function of the parametric bootstrap using the mechanism. Extensive experiments have verified that the two presented methods can enhance the accuracy of parameter learning.
Keywords:
Bayesian network
Parameter learning
Overfitting
Underfitting
Journal
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6.8
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540
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6.2W
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