Bayesian network is an effective tool for uncertainty knowledge presentation and inference. Bayesian network inference algorithm is one of the main fields in Bayesian network research. Currently, in almost every inference algorithm, the conditional probability distribution (CPD) of each node in a Bayesian network is represented in the form of conditional probability table (CPT). However, there is an exponential increase in the number of probability parameters of each CPT as the number of father nodes grows, which will cause an upsurge in the number of parameters in a Bayesian network and finally reduce the inference efficiency. To improve the inference efficiency of Bayesian network, the algebraic decision diagram (ADD) is proposed to represent the CPD of each node in a Bayesian network. Furthermore, by using the theory of ordered binary decision diagram, we analyze and verify the principle that ADD reduces the parameters of a Bayesian network by characterizing the context-specific independence among the parent-child nodes of the net. In addition, the algorithm for converting a CPT into its equivalent ADD is deduced. Eventually, the efficiency of ADD in parameter storage is validated by an example. It shows that for any Bayesian network with the context-specific independence, the parameters of the net can be reduced in the form of the equivalent ADD compared to the form of CPT, which provides a powerful tool for improving the inference efficiency of Bayesian network.
