Artificial intelligence applications could be more powerful and comprehensive by incorporating the ability of inference, which could be achieved by probabilistic inference over implicit relations. It is significant yet challenging to represent implicit relations among observed variables and latent ones like disease etiologies and user preferences. In this paper, we propose the BN with multiple latent variables (MLBN) as the framework for representing the dependence relations, where multiple latent variables are incorporated to describe multi-dimensional abstract concepts. However, the efficiency of MLBN learning and effectiveness of MLBN based applications are still nontrivial due to the presence of multiple latent variables. To this end, we first propose the constraint induced and Spark based algorithm for MLBN learning, as well as several optimization strategies. Moreover, we present the concept of variation degree and further design a subgraph based algorithm for incremental learning of MLBN. Experimental results suggest that our proposed MLBN model could represent the dependence relations correctly. Our proposed method outperforms some state-of-the-art competitors for personalized recommendation, and facilitates some typical approaches to achieve better performance.

通过结合推理能力，人工智能应用可以更加强大和全面，这可以通过隐式关系的概率推理来实现。表示观察变量与疾病病因和用户偏好等潜在变量之间的隐含关系非常重要，但具有挑战性。在本文中，我们提出了具有多个潜在变量的BN（MLBN）作为表示依赖关系的框架，其中结合多个潜在变量来描述多维抽象概念。然而，由于存在多个潜在变量，MLBN 学习的效率和基于 MLBN 的应用程序的有效性仍然很重要。为此，我们首先提出了约束诱导和基于 Spark 的 MLBN 学习算法，以及几种优化策略。此外，我们提出了变异度的概念，并进一步设计了一种基于子图的 MLBN 增量学习算法。实验结果表明，我们提出的 MLBN 模型可以正确表示依赖关系。我们提出的方法在个性化推荐方面优于一些最先进的竞争对手，并促进了一些典型方法获得更好的性能。