Federated multi-task Bayesian network learning in the presence of overlapping and distinct variables

Bayesian Network (BN) is a powerful tool for causal dependence relationship discoveries of multivariate data. This article proposes a federated multi-task learning framework for BNs with overlapping and distinct variables. First, an additive structural causal model is proposed to describe the nonparametric causal dependence structure for each client’s BN. Then by assuming different clients can have similar, yet not identical, causal dependence structures, a two-step federated multi-task learning framework is formulated for parameter learning of different clients, which can protect data privacy in the meanwhile. In the first step, each client updates its local BN parameters with its own data. In the second step, the central server updates global parameters. The two steps iterate until converge. Numerical studies and a case study of a three-phase flow facility data demonstrate the efficacy of our proposed method.