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On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis

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  • Bing Li
  • Hyonho Chun
  • Hongyu Zhao

Abstract

We introduce a nonparametric method for estimating non-Gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among random vectors that resembles the logical structure of conditional independence. Additive conditional independence allows us to use one-dimensional kernel regardless of the dimension of the graph, which not only avoids the curse of dimensionality but also simplifies computation. It also gives rise to a parallel structure to the Gaussian graphical model that replaces the precision matrix by an additive precision operator. The estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case, but outperform it when the Gaussian copula assumption is violated. We compare the new method with existing ones by simulations and in genetic pathway analysis. Supplementary materials for this article are available online.

Suggested Citation

  • Bing Li & Hyonho Chun & Hongyu Zhao, 2014. "On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1188-1204, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1188-1204
    DOI: 10.1080/01621459.2014.882842
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    Citations

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    Cited by:

    1. Sheng, Tianhong & Li, Bing & Solea, Eftychia, 2023. "On skewed Gaussian graphical models," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Kuang-Yao Lee & Bing Li & Hongyu Zhao, 2016. "Variable selection via additive conditional independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1037-1055, November.
    3. Virta, Joni & Li, Bing & Nordhausen, Klaus & Oja, Hannu, 2020. "Independent component analysis for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    4. Kim, Kyongwon, 2022. "On principal graphical models with application to gene network," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    5. Song, Jun & Li, Bing, 2021. "Nonlinear and additive principal component analysis for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    6. Kuang‐Yao Lee & Lexin Li, 2022. "Functional structural equation model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 600-629, April.

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