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    On an additive partial correlation operator and nonparametric estimation of graphical models

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    On an additive partial correlation ...
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    Genre
    Post-print
    Date
    2016-09-01
    Author
    Lee, KY
    Li, B
    Zhao, H
    Subject
    Additive conditional covariance operator
    Additive conditional independence
    Copula
    Gaussian graphical model
    Partial correlation
    Reproducing kernel
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5032
    
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    DOI
    10.1093/biomet/asw028
    Abstract
    © 2016 Biometrika Trust. We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional independence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance.
    Citation to related work
    Oxford University Press (OUP)
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    Biometrika
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    http://dx.doi.org/10.34944/dspace/5014
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