Distributed fusion-based algorithms for learning high-dimensional Bayesian Networks: Testing ring and star topologies

Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although there are approaches based on horizontal (instances) or vertical (variables) partitioning in the literature, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. This paper proposes a parallel distributed framework that uses GES as its local learning algorithm, obtaining results similar to those of GES and guaranteeing its theoretical properties but requiring less execution time. The framework involves splitting the set of all possible edges into clusters and constraining each framework node to only work with the received subset of edges. The global learning process is an iterative algorithm that carries out rounds until a convergence criterion is met. We have designed a ring and a star topology to distribute node connections. Regardless of the topology, each node receives a BN as input; it then fuses it with its own BN model and uses the result as the starting point for a local learning process, limited to its own subset of edges. Once finished, the result is then sent to another node as input. Experiments were carried out on a large repertory of domains, including large BNs up to more than 1000 variables. Our results demonstrate our proposal's effectiveness compared to GES and its fast version (fGES), generating high-quality BNs in less execution time.