  This paper proposes a model learning Semi-parametric relationships in an
Expert Bayesian Network (SEBN) with linear parameter and structure constraints.
We use Gaussian Processes and a Horseshoe prior to introduce minimal nonlinear
components. To prioritize modifying the expert graph over adding new edges, we
optimize differential Horseshoe scales. In real-world datasets with unknown
truth, we generate diverse graphs to accommodate user input, addressing
identifiability issues and enhancing interpretability. Evaluation 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.
