Journal article

A generalization of hierarchical exchangeability on trees to directed acyclic graphs

Abstract:: 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 ℕ|𝑉| for some DAG 𝐺=(𝑉,𝐸), and its exchangeability structure is governed by the edge set 𝐸. We prove a representation theorem for such arrays which generalizes the Aldous-Hoover and Austin–Panchenko representation theorems.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Jung, P., Lee, J., Staton, S., & Yang, H. (2021). A generalization of hierarchical exchangeability on trees to directed acyclic graphs. Annales Henri Lebesgue, 4, 325–368.

MLA Style

Jung, P., et al. “A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs.” Annales Henri Lebesgue, vol. 4, ENS Rennes, 2021, pp. 325–68.

Chicago Style

Jung, P, J Lee, S Staton, and H Yang. 2021. “A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs.” Annales Henri Lebesgue 4: 325–68.
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Files:: AHL_2021__4__325_0.pdf

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Publisher copy:: 10.5802/ahl.74

Authors

+ Jung, P More by this author

Role:: Author

+ Lee, J More by this author

Role:: Author

+ Staton, S More by this author

Division:: MPLS
Department:: Computer Science
Role:: Author

+ Yang, H More by this author

Role:: Author

+ Engineering and Physical Sciences Research Council More from this funder

Grant:: EP/N007387/1

+ Royal Society More from this funder

Grant:: UF130290

Publisher:: ENS Rennes
Journal:: Annales Henri Lebesgue More from this journal
Volume:: 4
Pages:: 325-368
Publication date:: 2021-01-18
Acceptance date:: 2020-04-15
DOI:: 10.5802/ahl.74
EISSN:: 2644-9463

Language:: English
Keywords:: exchangeability

Bayesian nonparametrics

AldousHoover representation

hierarchical exchangeability

FFR

de Finetti representation
Pubs id:: 1102319
Local pid:: pubs:1102319
Deposit date:: 2020-04-29

Terms of use

Copyright holder:: Jung et al
Copyright date:: 2020
Rights statement:: Published under license CC BY 4.0.

Licence:: CC Attribution (CC BY)

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