Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. Within the context of Bayesian Networks, a practical and surprisingly successful solution to this learning problem is achieved by adopting score-functions optimisation schema, augmented with multiple restarts to avoid local optima. Yet, the conditions under which such strategies work well are poorly understood, and there are also some intrinsic limitations to learning the directionality of the interaction among the variables. Following an early intuition of Friedman and Koller, we propose to decouple the learning problem into two steps: first, we identify a partial ordering among input variables which constrains the structural learning problem, and then propose an effective bootstrap-based algorithm to simulate augmented data sets, and select the most important dependencies among the variables. By using several synthetic data sets, we show that our algorithm yields better recovery performance than the state of the art, increasing the chances of identifying a globally-optimal solution to the learning problem, and solving also well-known identifiability issues that affect the standard approach. We use our new algorithm to infer statistical dependencies between cancer driver somatic mutations detected by high-throughput genome sequencing data of multiple colorectal cancer patients. In this way, we also show how the proposed methods can shade new insights about cancer initiation, and progression. Code: https://github.com/caravagn/Bootstrap-based-Learning
