Most challenging problems in the life sciences, natural sciences and engineering involve disentangling complex networks of probabilistic and causal relationships among heterogeneous, large data sources. This endeavour poses three challenges: devising algorithms that can scale to high dimensions; formulating models that are auditable and interpretable, but also flexible; and balance interpretability against predictive accuracy. Bayesian networks strive to address these concerns, and can be learned efficiently from both big data and high-dimensional data. In this talk I will discuss some of my recent research on computational and information-theoretic aspects of structure learning, touching on the challenges of incomplete and correlated observations and more in general on the nature of prediction in machine
learning models.