DomainLiftability of Relational Marginal Polytopes
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:22842292, 2020.
Abstract
We study computational aspects of "relational marginal polytopes" which are statistical relational learning counterparts of marginal polytopes, wellknown from probabilistic graphical models. Here, given some firstorder logic formula, we can define its relational marginal statistic to be the fraction of groundings that make this formula true in a given possible world. For a list of firstorder logic formulas, the relational marginal polytope is the set of all points that correspond to expected values of the relational marginal statistics that are realizable. In this paper we study the following two problems: (i) Do domainliftability results for the partition functions of Markov logic networks (MLNs)carry over to the problem of relational marginal polytope construction? (ii) Is the relational marginal polytope containment problem hard under some plausible complexitytheoretic assumptions? Our positive results have consequences for lifted weight learning of MLNs. In particular, we show that weight learning of MLNs is domainliftable whenever the computation of the partition function of the respective MLNs is domainliftable (this result has not been rigorously proven before).
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