exchangeable arrays
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Author(s):  
Harold D. Chiang ◽  
Kengo Kato ◽  
Yuya Sasaki


2021 ◽  
Vol 49 (2) ◽  
Author(s):  
Laurent Davezies ◽  
Xavier D’Haultfœuille ◽  
Yannick Guyonvarch


Author(s):  
Manfred Jaeger ◽  
Oliver Schulte

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 learning (SRL) frameworks, these models are not projective in the sense that the marginal of the distribution 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 statistically consistent learning from sub-sampled relational structures. In earlier work some simple fragments 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 paper we fill this gap: exploiting representation theorems 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 distribution 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 inference to general relational signatures.



2016 ◽  
Vol 114 ◽  
pp. 54-59 ◽  
Author(s):  
Alexander Volfovsky ◽  
Edoardo M. Airoldi


2004 ◽  
Vol 70 (1) ◽  
pp. 95-108
Author(s):  
B. Gail Ivanoff ◽  
N.C. Weber
Keyword(s):  


Bernoulli ◽  
2000 ◽  
Vol 6 (2) ◽  
pp. 285 ◽  
Author(s):  
Peter McCullagh
Keyword(s):  


Author(s):  
B. G. Ivanoff ◽  
N. C. Weber

AbstractKallenberg [2] introduced the concept of F-exchangeable sequences of random variables and produced some characterizations of F-exchangeability in terms of stopping times. In this paper ways of extending the concept of F-exchangeability to doubly indexed arrays of random variables are explored and some characterizations obtained for row and column exchangebale arrays, weakly exchangeable arrays and separately exchangeable continuous processes.



1995 ◽  
Vol 55 (2) ◽  
pp. 133-148 ◽  
Author(s):  
B.G. Ivanoff ◽  
N.C. Weber


1992 ◽  
Vol 40 (1-2) ◽  
pp. 1-22 ◽  
Author(s):  
B.G Ivanoff ◽  
N.C. Weber


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