This paper proposes a model learning Semi-parametric rela- tionships in an Expert Bayesian Network (SEBN) with linear parameter and structure constraints. We use Gaussian Pro- cesses and a Horseshoe prior to introduce minimal nonlin- ear components. To prioritize modifying the expert graph over adding new edges, we optimize differential Horseshoe scales. In real-world datasets with unknown truth, we gen- erate diverse graphs to accommodate user input, addressing identifiability issues and enhancing interpretability. Evalua- tion on synthetic and UCI Liver Disorders datasets, using metrics like structural Hamming Distance and test likelihood, demonstrates our models outperform state-of-the-art semi- parametric Bayesian Network model.

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