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Constrained likelihood for reconstructing a directed acyclic Gaussian graph

Author

Listed:
  • Yiping Yuan
  • Xiaotong Shen
  • Wei Pan
  • Zizhuo Wang

Abstract

SUMMARY Directed acyclic graphs are widely used to describe directional pairwise relations. Such relations are estimated by reconstructing a directed acyclic graph’s structure, which is challenging when the ordering of nodes of the graph is unknown. In such a situation, existing methods such as the neighbourhood and search-and-score methods have high estimation errors or computational complexities, especially when a local or sequential approach is used to enumerate edge directions by testing or optimizing a criterion locally, as a local method may break down even for moderately sized graphs. We propose a novel approach to simultaneously identifying all estimable directed edges and model parameters, using constrained maximum likelihood with nonconvex constraints. We develop a constraint reduction method that constructs a set of active constraints from super-exponentially many constraints. This, coupled with an alternating direction method of multipliers and a difference convex method, permits efficient computation for large-graph learning. We show that the proposed method consistently reconstructs identifiable directions of the true graph and achieves the optimal performance in terms of parameter estimation. Numerically, the method compares favourably with competitors. A protein network is analysed to demonstrate that the proposed method can make a difference in identifying the network’s structure.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:biomet:v:106:y:2019:i:1:p:109-125.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy057
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    Citations

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    Cited by:

    1. 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.
    2. Shi, Chengchun & Li, Lexin, 2022. "Testing mediation effects using logic of Boolean matrices," LSE Research Online Documents on Economics 108881, London School of Economics and Political Science, LSE Library.
    3. Li, Lexin & Shi, Chengchun & Guo, Tengfei & Jagust, William J., 2022. "Sequential pathway inference for multimodal neuroimaging analysis," LSE Research Online Documents on Economics 111904, London School of Economics and Political Science, LSE Library.
    4. Haoran Xue & Wei Pan, 2020. "Inferring causal direction between two traits in the presence of horizontal pleiotropy with GWAS summary data," PLOS Genetics, Public Library of Science, vol. 16(11), pages 1-30, November.
    5. Haoyu Wei & Hengrui Cai & Chengchun Shi & Rui Song, 2024. "On Efficient Inference of Causal Effects with Multiple Mediators," Papers 2401.05517, arXiv.org.

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