DomainSize Aware Markov Logic Networks
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Proceedings of Machine Learning Research, PMLR 89:32163224, 2019.
Abstract
Several domains in AI need to represent the relational structure as well as model uncertainty. Markov Logic is a powerful formalism which achieves this by attaching weights to formulas in finite firstorder logic. Though Markov Logic Networks (MLNs) have been used for a wide variety of applications, a significant challenge remains that weights do not generalize well when training domain sizes are different from those seen during testing. In particular, it has been observed that marginal probabilities tend to extremes in the limit of increasing domain sizes. As the first contribution of our work, we further characterize the distribution and show that marginal probabilities tend to a constant independent of weights and not always to extremes as was previously observed. As our second contribution, we present a principled solution to this problem by defining Domainsize Aware Markov Logic Networks (DAMLNs) which can be seen as reparameterizing the MLNs after taking domain size into consideration. For some simple but representative MLN formulas, we formally prove that probabilities defined by DAMLNs are well behaved. On a practical side, DAMLNs allow us to generalize the weights learned over smallsized training data to much larger domains. Experiments on three different benchmark MLNs show that our approach results in significant performance gains compared to existing methods.
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