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Duality of graphical models and tensor networks

Abstract:

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. We translate various notions under duality. For example, marginalization in a graphical model is dual to contraction in the tensor network. Algorithms also translate under duali...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1093/imaiai/iay009

Authors


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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Queens College
Role:
Author
Publisher:
Oxford University Press Publisher's website
Journal:
Information and Inference Journal website
Volume:
8
Issue:
2
Pages:
273-288
Publication date:
2018-06-21
Acceptance date:
2018-04-30
DOI:
EISSN:
2049-8772
ISSN:
2049-8764
Source identifiers:
1027140
Keywords:
Pubs id:
pubs:1027140
UUID:
uuid:274edc9a-687f-456f-ab69-86339bdb0524
Local pid:
pubs:1027140
Deposit date:
2019-07-27

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