期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 109, 期 507, 页码 1188-1204出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2014.882842
关键词
Additive precision operator; Additive conditional independence; Nonparanormal graphical model; Gaussian graphical model; Reproducing kernel Hilbert space; Copula; Covariance operator; Conditional independence
资金
- NSF [DMS-1106815, DMS-1107025, DMS-1106738]
- NIH [R01-GM59507, P01-CA154295]
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.
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