Relational Marginal Problems: Theory and Estimation

In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the parameters of relational models, which generalizes a well-known duality from the propositional setting. Third, by exploiting the relational marginal formulation, we present a statistically sound method to learn the parameters of relational models that will be applied in settings where the number of constants differs between the training and test data. Furthermore, based on a relational generalization of marginal polytopes, we characterize cases where the standard estimators based on feature's number of true groundings needs to be adjusted and we quantitatively characterize the consequences of these adjustments. Fourth, we prove bounds on expected errors of the estimated parameters, which allows us to lower-bound, among other things, the effective sample size of relational training data.

• Publication year

  2017

• Venue

  AAAI Conference on Artificial Intelligence

• Publication date

  2017-09-18

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1609/aaai.v32i1.12113arXiv 1709.05825
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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