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.

翻译：本文提出一种模型学习方法，用于在线性参数与结构约束下学习专家贝叶斯网络（SEBN）中的半参数关系。我们采用高斯过程与马蹄先验引入最小非线性成分。为优先修改专家图结构而非添加新边，我们优化了差异化马蹄尺度参数。针对真实世界未知底事实数据集，通过生成多样化图结构以适应用户输入，该方法有效解决了可辨识性问题并增强了可解释性。基于结构汉明距离与测试似然等指标，在合成数据集及UCI肝脏疾病数据集上的评估表明，我们的模型性能优于当前最先进的半参数贝叶斯网络模型。