Domain Aware Markov Logic Networks
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Combining logic and probability has been a long standing goal of AI. Markov Logic Networks (MLNs) achieve this by attaching weights to formulae 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 learning the parameters of the model. This results in incorrect (often extreme) probabilities when testing on domain sizes different from those seen during training times. In this paper, we propose Domain Aware Markov logic Networks (DA-MLNs) which present a principled solution to this problem, by dividing the ground feature weight by a function of the number of connections each ground atom (in the feature) is involved in, when defining the ground Markov network distribution. We show that standard MLNs fall out as a special case of our formalism when this function is a constant (and is equal to 1). Experiments on a benchmark domain show that our approach results in significantly higher accuracies (compared to baselines) when testing on domain sizes different than those seen during training.
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