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Structure learning in Bayesian Networks using regular vines

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  • Hobæk Haff, Ingrid
  • Aas, Kjersti
  • Frigessi, Arnoldo
  • Lacal, Virginia

Abstract

Learning the structure of a Bayesian Network from multidimensional data is an important task in many situations, as it allows understanding conditional (in)dependence relations which in turn can be used for prediction. Current methods mostly assume a multivariate normal or a discrete multinomial model. A new greedy learning algorithm for continuous non-Gaussian variables, where marginal distributions can be arbitrary, as well as the dependency structure, is proposed. It exploits the regular vine approximation of the model, which is a tree-based hierarchical construction with pair-copulae as building blocks. It is shown that the networks obtainable with our algorithm belong to a certain subclass of chordal graphs. Chordal graphs representations are often preferred, as they allow very efficient message passing and information propagation in intervention studies. It is illustrated through several examples and real data applications that the possibility of using non-Gaussian margins and a non-linear dependency structure outweighs the restriction to chordal graphs.

Suggested Citation

  • Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo & Lacal, Virginia, 2016. "Structure learning in Bayesian Networks using regular vines," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 186-208.
  • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:186-208
    DOI: 10.1016/j.csda.2016.03.003
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    References listed on IDEAS

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    Cited by:

    1. KIM, Junyung & ZHAO, Xingang & SHAH, Asad Ullah Amin & KANG, Hyun Gook, 2021. "System risk quantification and decision making support using functional modeling and dynamic Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    2. Quanrui Song & Jianxu Liu & Songsak Sriboonchitta, 2019. "Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    3. Müller, Dominik & Czado, Claudia, 2019. "Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 211-232.
    4. Aas Kjersti & Nagler Thomas & Jullum Martin & Løland Anders, 2021. "Explaining predictive models using Shapley values and non-parametric vine copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 62-81, January.
    5. Zhu, Kailun & Kurowicka, Dorota, 2022. "Regular vines with strongly chordal pattern of (conditional) independence," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    6. Pierpaolo D’Urso & Vincenzina Vitale, 2021. "Modeling Local BES Indicators by Copula-Based Bayesian Networks," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(3), pages 823-847, February.

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