Duality of Graphical Models and Tensor Networks
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Abstract (arXiv)
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 duality. We show that belief propagation corresponds to a known algorithm for tensor network contraction. This article is a reminder that the research areas of graphical models and tensor networks can benefit from interaction.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Oct 2017.
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Citing papers per year: 2021: 3; 2022: 2; 2023: 3; 2024: 4; 2025: 1; 2026: 2.
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- 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
- 2021Tensor networks and efficient descriptions of classical datacited by 13
- 2021Probabilistic Graphical Models and Tensor Networks: A Hybrid Frameworkcited by 5
- 2022You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networkscited by 4
- 2022High-dimensional density estimation with tensorizing flowcited by 4
- 2024Probabilistic Inference in the Era of Tensor Networks and Differential Programmingcited by 4
- 2023The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networkscited by 2
- 2023Probabilistic Regular Tree Priors for Scientific Symbolic Reasoningcited by 1
- 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learningcited by 1
- 2024Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networkscited by 1
- 2021Global sensitivity analysis in probabilistic graphical modelscited by 0
- 2024Tensor Network Estimation of Distribution Algorithmscited by 0
3 more
- 2025Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progresscited by 0
- 2026TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Traincited by 0
- 2026On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networkscited by 0
- 2026On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks20 Sep 2026
- 2026TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Train5 Jan 2026
- 2025Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progress11 Mar 2025
- 2024Tensor Network Estimation of Distribution Algorithms27 Dec 2024
- 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?12 Sep 2024
- 2024Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks9 Jun 2024
- 2024Probabilistic Inference in the Era of Tensor Networks and Differential Programming22 May 2024
- 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning28 Jul 2023
- 2023Probabilistic Regular Tree Priors for Scientific Symbolic Reasoning14 Jun 2023
- 2023The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks1 Feb 2023
- 2022High-dimensional density estimation with tensorizing flow1 Dec 2022
- 2022You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks17 Jun 2022
3 more
- 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
- 2021Tensor networks and efficient descriptions of classical datacited by 13
- 2021Probabilistic Graphical Models and Tensor Networks: A Hybrid Frameworkcited by 5
- 2022You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networkscited by 4
- 2022High-dimensional density estimation with tensorizing flowcited by 4
- 2024Probabilistic Inference in the Era of Tensor Networks and Differential Programmingcited by 4
- 2023The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networkscited by 2
- 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learningcited by 1
- 2024Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networkscited by 1
- 2021Global sensitivity analysis in probabilistic graphical modelscited by 0
- 2024Tensor Network Estimation of Distribution Algorithmscited by 0
- 2025Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progresscited by 0
12 most cited of 14 All 14 (JSON)
- 2026On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks20 Sep 2026
- 2026TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Train5 Jan 2026
- 2025Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progress11 Mar 2025
- 2024Tensor Network Estimation of Distribution Algorithms27 Dec 2024
- 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?12 Sep 2024
- 2024Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks9 Jun 2024
- 2024Probabilistic Inference in the Era of Tensor Networks and Differential Programming22 May 2024
- 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning28 Jul 2023
- 2023The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks1 Feb 2023
- 2022High-dimensional density estimation with tensorizing flow1 Dec 2022
- 2022You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks17 Jun 2022
- 2021Global sensitivity analysis in probabilistic graphical models7 Oct 2021
12 newest of 14 All 14 (JSON)