Lightning-speed Structure Learning of Nonlinear Continuous Networks

Graphical models are widely used to reason about high-dimensional domains. Yet, learning the structure of the model from data remains a formidable challenge, particularly in complex continuous domains. We present a highly accelerated structure learning approach for continuous densities based on the recently introduced Copula Bayesian Network representation. For two common copula families, we prove that the expected likelihood of a building block edge in the model is monotonic in Spearman’s rank correlation measure. We also show numerically that the same relationship holds for many other copula families. This allows us to perform structure learning while bypassing costly parameter estimation as well as explicit computation of the log-likelihood function. We demonstrate the merit of our approach for structure learning in three varied real-life domains. Importantly, the computational benefits are such that they open the door for practical scaling-up of structure learning in complex nonlinear continuous domains.