Efficient comparison of independence structures of log-linear models

Log-linear models are a family of probability distributions which capture relationships between variables, including context-specific independencies. Many approaches exist for automatic learning of their independence structures from data, although the only known methods for evaluating these approaches are indirect measures of their complete density. This requires additional learning of numerical parameters, and introduces distortions when used for comparing structures. This work addresses this issue by presenting a measure for the direct and efficient comparison of independence structures of log-linear models. We present proof that the measure is a metric, and a method for its computation that is efficient in the number of variables of the domain. Efficiency in the number of features in the models is not guaranteed and will be the subject of future work.