Transformer Based Bayesian Network Embedding for Efficient Multiple Probabilistic Inferences

Bayesian network (BN) is a directed acyclic graph (DAG) representing the dependence relations among random variables with conditional probability tables (CPTs). The efficiency and accuracy of multiple probabilistic inferences in BN could not be guaranteed by most of the existing approximate inference methods. To address this issue, we propose the methods of Transformer based BN embedding (TBNE) and TBNE based probabilistic inferences. Specifically, we first adopt mutual information to measure the weight of parent-child node pairs and transform BN into multiple bidirectional weighted graphs (BWGs), while preserving the DAG and CPTs. Then, we redesign the Transformer model by incorporating the node importance and shortest path encodings, and extend the self-attention module of Transformer to generate node embeddings of BWGs. Following, we cast the probabilistic inference as the decoding information maximization of the path in BN from the perspective of information theory. Finally, we give an efficient algorithm for multiple probabilistic inferences by calculating embedding similarities between evidence and query nodes in BN. Experimental results show that our inference method is more efficient than the state-of-the-art competitors by several orders of magnitude while maintaining almost the same results.