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Replicates in high dimensions, with applications to latent variable graphical models

Author

Listed:
  • Kean Ming Tan
  • Yang Ning
  • Daniela M. Witten
  • Han Liu

Abstract

In classical statistics, much thought has been put into experimental design and data collection. In the high-dimensional setting, however, experimental design has been less of a focus. In this paper, we stress the importance of collecting multiple replicates for each subject in the high-dimensional setting. We consider learning the structure of a graphical model with latent variables, under the assumption that these variables take a constant value across replicates within each subject. By collecting multiple replicates for each subject, we can estimate the conditional dependence relationships among the observed variables given the latent variables. To test the hypothesis of conditional independence between two observed variables, we propose a pairwise decorrelated score test. Theoretical guarantees are established for parameter estimation and for this test. We show that our method is able to estimate latent variable graphical models more accurately than some existing methods, and we apply it to a brain imaging dataset.

Suggested Citation

  • Kean Ming Tan & Yang Ning & Daniela M. Witten & Han Liu, 2016. "Replicates in high dimensions, with applications to latent variable graphical models," Biometrika, Biometrika Trust, vol. 103(4), pages 761-777.
  • Handle: RePEc:oup:biomet:v:103:y:2016:i:4:p:761-777.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw050
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Byrd, Michael & Nghiem, Linh H. & McGee, Monnie, 2021. "Bayesian regularization of Gaussian graphical models with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Li‐Pang Chen & Grace Y. Yi, 2021. "Analysis of noisy survival data with graphical proportional hazards measurement error models," Biometrics, The International Biometric Society, vol. 77(3), pages 956-969, September.

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