Copula Grow-Shrink Algorithm for Structural Learning

The PC algorithm is the most known constraint-based algorithm for learning a directed acyclic graph using conditional independence tests. For Gaussian distributions the tests are based on Pearson correlation coefficients. PC algorithm for data drawn from a Gaussian copula model, Rank PC, has been recently introduced and is based on the Spearman correlation. Here, we present a modified version of the Grow-Shrink algorithm, named Copula Grow-Shrink; it is based on the recovery of the Markov blanket and on the Spearman correlation. By simulations it is shown that the Copula Grow-Shrink algorithm performs better than the PC and the Rank PC algorithms, according to the structural Hamming distance. Finally, the new algorithm is applied to Italian energy market data.