Bayesian Network (BN) is one of the most important methods for representing and inferring with uncertainty knowledge

and also a powerful theory model within the community of artificial intelligence.To solve the drawbacks of hybrid methods for learning BNs which are easy to fall into local optimum and unreliable for learning large data set

we propose a novel hybrid algorithm for learning BN equivalence classes which combines ideas from maximal prime decomposition (MPD) of graph theory

conditional independence (CI) tests

and local search-and-score techniques in an effective way.It first reconstructs the undirected independence graph of a BN and then performs MPD to transform the undirected graph into its subgraphs.Finally

the new algorithm uses only lower-order CI tests and local BDeu score to check the v-structure of each subgraph.Theoretical and experimental results show that the proposed algorithm is correctness and effective.