A partial correlation-based Bayesian network structure learning algorithm under linear SEM

A new algorithm, the PCB (partial correlation-based) algorithm, is presented for Bayesian network structure learning. The algorithm effectively combines ideas from local learning with partial correlation techniques. It reconstructs the skeleton of a Bayesian network based on partial correlation and then performs a greedy hill-climbing search to orient the edges. Specifically, we make three contributions. First, we prove that in a linear SEM (simultaneous equation model) with uncorrelated errors, when the datasets are generated by linear SEM, subject to arbitrary distribution disturbances, we can use partial correlation as the criterion of the CI test. Second, we perform a series of experiments to find the best threshold value of the partial correlation. Finally, we show how partial correlation can be used in Bayesian network structure learning under linear SEM. The effectiveness of the method is compared with current state of the art methods on eight networks. A simulation shows that the PCB algorithm outperforms existing algorithms in both accuracy and run time.