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Testing directed acyclic graph via structural, supervised and generative adversarial learning

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  • Shi, Chengchun
  • Zhou, Yunzhe
  • Li, Lexin

Abstract

In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods often impose some specific model structures such as linear models or additive models, and assume independent data observations. Our proposed test instead allows the associations among the random variables to be nonlinear and the data to be time-dependent. We build the test based on some highly flexible neural networks learners. We establish the asymptotic guarantees of the test, while allowing either the number of subjects or the number of time points for each subject to diverge to infinity. We demonstrate the efficacy of the test through simulations and a brain connectivity network analysis. Supplementary materials for this article are available online.

Suggested Citation

  • Shi, Chengchun & Zhou, Yunzhe & Li, Lexin, 2023. "Testing directed acyclic graph via structural, supervised and generative adversarial learning," LSE Research Online Documents on Economics 119446, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119446
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    File URL: http://eprints.lse.ac.uk/119446/
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    References listed on IDEAS

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    3. Chunlin Li & Xiaotong Shen & Wei Pan, 2020. "Likelihood Ratio Tests for a Large Directed Acyclic Graph," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1304-1319, July.
    4. Nikolaos Kourogenis & Nikitas Pittis, 2011. "Mixing Conditions, Central Limit Theorems, and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences," Econometric Reviews, Taylor & Francis Journals, vol. 30(1), pages 88-108.
    5. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
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    7. Shi, Chengchun & Xu, Tianlin & Bergsma, Wicher & Li, Lexin, 2021. "Double generative adversarial networks for conditional independence testing," LSE Research Online Documents on Economics 112550, London School of Economics and Political Science, LSE Library.
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    More about this item

    Keywords

    brain connectivity networks; directed acrylic graph; hypothesis testing; generative adversarial networks; multilayer perceptron neural networks; Hypothesis testing; CIF-2102227; R01AG061303; R01AG062542; EP/W014971/1;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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