Domain Aware Markov Logic Networks

Combining logic and probability has been a long stand- ing goal of AI research. Markov Logic Networks (MLNs) achieve this by attaching weights to formulas in first-order logic, and can be seen as templates for constructing features for ground Markov networks. Most techniques for learning weights of MLNs are domain-size agnostic, i.e., the size of the domain is not explicitly taken into account while learn- ing the parameters of the model. This often results in ex- treme probabilities when testing on domain sizes different from those seen during training. In this paper, we propose Domain Aware Markov logic Networks (DA-MLNs) which present a principled solution to this problem. While defin- ing the ground network distribution, DA-MLNs divide the ground feature weight by a scaling factor which is a function of the number of connections the ground atoms appearing in the feature are involved in. We show that standard MLNs fall out as a special case of our formalism when this func- tion evaluates to a constant equal to 1. Experiments on the benchmark Friends & Smokers domain show that our ap- proach results in significantly higher accuracies compared to existing methods when testing on domains whose sizes different from those seen during training.