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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, 2024. "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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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. 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.
    3. 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.
    4. Yiping Yuan & Xiaotong Shen & Wei Pan & Zizhuo Wang, 2019. "Constrained likelihood for reconstructing a directed acyclic Gaussian graph," Biometrika, Biometrika Trust, vol. 106(1), pages 109-125.
    5. 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.
    6. Huitong Qiu & Fang Han & Han Liu & Brian Caffo, 2016. "Joint estimation of multiple graphical models from high dimensional time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 487-504, March.
    7. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    8. 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.
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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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