A Complete Characterization of Projectivity for Statistical Relational Models

Manfred Jaeger, Oliver Schulte

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Abstrakt

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.
OriginalsprogEngelsk
TitelProceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI-20)
ForlagInternational Joint Conferences on Artificial Intelligence
Publikationsdato2020
Sider4283-4290
ISBN (Elektronisk)978-0-9992411-6-5
DOI
StatusUdgivet - 2020
Begivenhed29th International Joint Conference on Artificial Intelligence, IJCAI 2020 - Yokohama, Japan
Varighed: 1 jan. 2021 → …

Konference

Konference29th International Joint Conference on Artificial Intelligence, IJCAI 2020
LandJapan
ByYokohama
Periode01/01/2021 → …
SponsorInternational Joint Conferences on Artifical Intelligence (IJCAI)

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