Domain Aware Markov Logic Networks
This addresses a domain-size sensitivity issue in probabilistic logic models, offering a principled solution for more robust inference across varying domain scales, though it appears incremental as it builds directly on existing MLN frameworks.
The paper tackles the problem of Markov Logic Networks (MLNs) producing extreme probabilities when tested on domain sizes different from training by proposing Domain Aware MLNs (DA-MLNs), which scale ground feature weights based on domain connections, resulting in significantly higher accuracies in experiments on the Friends & Smokers benchmark.
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.