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Graph estimation with joint additive models

Author

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  • Arend Voorman
  • Ali Shojaie
  • Daniela Witten

Abstract

In recent years, there has been considerable interest in estimating conditional independence graphs in high dimensions. Most previous work assumed that the variables are multivariate Gaussian or that the conditional means of the variables are linearly related. Unfortunately, if these assumptions are violated, the resulting conditional independence estimates can be inaccurate. We propose a semiparametric method, graph estimation with joint additive models, which allows the conditional means of the features to take an arbitrary additive form. We present an efficient algorithm for computation of our estimator, and prove that it is consistent. We extend our method to estimation of directed graphs with known causal ordering. Using simulated data, we show that our method performs better than existing methods when there are nonlinear relationships among the features, and is comparable to methods that assume multivariate normality when the conditional means are linear. We illustrate our method on a cell signalling dataset.

Suggested Citation

  • Arend Voorman & Ali Shojaie & Daniela Witten, 2014. "Graph estimation with joint additive models," Biometrika, Biometrika Trust, vol. 101(1), pages 85-101.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:85-101.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast053
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    Cited by:

    1. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Jie Jian & Peijun Sang & Mu Zhu, 2024. "Two Gaussian Regularization Methods for Time-Varying Networks," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(4), pages 853-873, December.
    3. Chun, Hyonho & Lee, Myung Hee & Fleet, James C. & Oh, Ji Hwan, 2016. "Graphical models via joint quantile regression with component selection," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 162-171.
    4. Guo, Shaojun & Qiao, Xinghao, 2023. "On consistency and sparsity for high-dimensional functional time series with application to autoregressions," LSE Research Online Documents on Economics 114638, London School of Economics and Political Science, LSE Library.
    5. Hao Mei & Ruofan Jia & Guanzhong Qiao & Zhenqiu Lin & Shuangge Ma, 2023. "Human disease clinical treatment network for the elderly: analysis of the medicare inpatient length of stay and readmission data," Biometrics, The International Biometric Society, vol. 79(1), pages 404-416, March.
    6. Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    7. Linh H. Nghiem & Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2022. "Estimation of graphical models for skew continuous data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1811-1841, December.

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