Efficient comparison of independence structures of log-linear models

Log-linear models are a family of probability distributions which capture a variety of relationships between variables, including context-specific independencies. There are a number of approaches for automatic learning of their independence structures from data, although to date, no efficient method exists for evaluating these approaches directly in terms of the structures of the models. The only known methods evaluate these approaches indirectly through the complete model produced, that includes not only the structure but also the model parameters, introducing potential distortions in the comparison. This work presents such a method, that is, a measure for the direct comparison of the independence structures of log-linear models, inspired by the Hamming distance comparison method used in undirected graphical models. The measure presented can be efficiently computed in terms of the number of variables of the domain, and is proven to be a distance metric.