Relational marginal problems: theory and estimation

Kuzelka, Ondrej, Wang, Yuyi, Davis, Jesse and Schockaert, Steven 2018. Relational marginal problems: theory and estimation. Presented at: 32nd AAAI Conference on Artificial Intelligence, New Orleans, USA, 2-7 February 2018.

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Abstract

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.

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Completion
Status:	Unpublished
Schools:	Computer Science & Informatics
Funders:	ERC and Leverhulme Trust
Related URLs:	Organisation
Date of First Compliant Deposit:	20 November 2017
Last Modified:	22 Jun 2018 08:50
URI:	http://orca.cf.ac.uk/id/eprint/106738

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