A Complete Characterization of Projectivity for Statistical Relational Models

Manfred Jaeger, Oliver Schulte

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

Abstract

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learn- ing (SRL) frameworks, these models are not pro- jective in the sense that the marginal of the distribu- tion for size-n structures on induced substructures of size k < n is equal to the given distribution for size-k structures. Projectivity is very beneficial in that it directly enables lifted inference and statis- tically consistent learning from sub-sampled rela- tional structures. In earlier work some simple frag- ments of SRL languages have been identified that represent projective models. However, no complete characterization of, and representation framework for projective models has been given. In this pa- per we fill this gap: exploiting representation theo- rems for infinite exchangeable arrays we introduce a class of directed graphical latent variable models that precisely correspond to the class of projective relational models. As a by-product we also obtain a characterization for when a given distribution over size-k structures is the statistical frequency distri- bution of size-k substructures in much larger size- n structures. These results shed new light onto the old open problem of how to apply Halpern et al.’s “random worlds approach” for probabilistic infer- ence to general relational signatures.
Original languageEnglish
Title of host publicationProceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI-20)
PublisherInternational Joint Conferences on Artificial Intelligence
Publication date2020
Pages4283-4290
ISBN (Electronic)978-0-9992411-6-5
DOIs
Publication statusPublished - 2020

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