期刊
STATISTICA SINICA
卷 29, 期 1, 页码 479-504出版社
STATISTICA SINICA
DOI: 10.5705/ss.202017.0076
关键词
Correlated samples; false discovery rate; matrix-variate Gaussian graphical models; multiple tests; support recovery
资金
- Alibaba innovation research award
- Bloomberg data science research award
- NSFC [11431006, 11690013]
- Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, Shanghai Shuguang Program, Youth Talent Support Program, 973 Program [2015CB856004]
- Australian Research Council
Matrix-variate Gaussian graphical models (GGM) have been widely used for modeling matrix-variate data. Since the support of sparse precision matrix represents the conditional independence graph among matrix entries, conducting support recovery yields valuable information. A commonly used approach is the penalized log-likelihood method. However, due to the complicated structure of precision matrices in the form of Kronecker products, the log-likelihood is non-convex, which presents challenges for both computation and theoretical analysis. In this paper, we propose an alternative approach by formulating the support recovery problem as a multiple testing problem. A new test statistic is developed and, based on that, we use the popular Benjamini and Hochberg's procedure to control false discovery rate (FDR) asymptotically. Our method involves only convex optimization, making it computationally attractive. Theoretically, our method allows very weak conditions and, even when the sample size is finite and the dimensions go to infinity, the asymptotic normality of the test statistics and FDR control can still be guaranteed. We further provide the power analysis result. The finite sample performance of the proposed method is illustrated with simulations and real data analysis.
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