A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs

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Motivated by the problem of designing inference-friendly Bayesian nonparametric models in probabilistic programming languages, we introduce a general class of partially exchangeable random arrays which generalizes the notion of hierarchical exchangeability introduced in Austin and Panchenko (2014). We say that our partially exchangeable arrays are DAG-exchangeable since their partially exchangeable structure is governed by a collection of Directed Acyclic Graphs. More specifically, such a random array is indexed by โ„•|๐‘‰| for some DAG ๐บ=(๐‘‰,๐ธ), and its exchangeability structure is governed by the edge set ๐ธ. We prove a representation theorem for such arrays which generalizes the Aldous-Hoover and Austinโ€“Panchenko representation theorems.
Publisher
Centre Mersenne
Issue Date
2021-01
Language
English
Citation

Annales Henri Lebesgue, v.4, pp.325 - 368

ISSN
2644-9463
DOI
10.5802/ahl.74
URI
http://hdl.handle.net/10203/281746
Appears in Collection
MA-Journal Papers(์ €๋„๋…ผ๋ฌธ)CS-Journal Papers(์ €๋„๋…ผ๋ฌธ)
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