A quantitative assessment of the effect of different algorithmic schemes to the task of learning the structure of Bayesian Networks

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions and turned out to be a wellknown NP -hard problem and, hence, approximations are required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed study of the different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the characteristics of different widespread scores proposed for the inference and the statistical pitfalls within them.