Sparse Matrix Graphical Models

作者：Leng Chenlei^*; Tang Cheng Yong

来源：Journal of the American Statistical Association, 2012, 107(499): 1187-1200.

DOI：10.1080/01621459.2012.706133

• Conditional independence
• Matrix-variate normal distribution
• Penalized likelihood
• Sparsistency
• Sparsity

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this article, we propose a novel sparse matrix graphical model for these types of statistical problems. By penalizing, respectively, two precision matrices corresponding to the rows and columns, our method yields a sparse matrix graphical model that synthetically characterizes the underlying conditional independence structure. Our model is more parsimonious and is practically more interpretable than the conventional sparse vector-variate graphical models. Asymptotic analysis shows that our penalized likelihood estimates enjoy better convergent rates than that of the vector-variate graphical model. The finite sample performance of the proposed method is illustrated via extensive simulation studies and several real datasets analysis.

• 出版日期2012-9