High - dimensional semiparametric bigraphical models


In multivariate analysis, a Gaussian bigraphical model is commonly used for modelling matrixvalued data. In this paper, we propose a semiparametric extension of the Gaussian bigraphical model, called the nonparanormal bigraphical model. A projected nonparametric rank-based regularization approach is employed to estimate sparse precision matrices and produce graphs under a penalized likelihood framework. Theoretically, our semiparametric procedure achieves the parametric rates of convergence for both matrix estimation and graph recovery. Empirically, our approach outperforms the parametric Gaussian model for non-Gaussian data and is competitive with its parametric counterpart for Gaussian data. Extensions to the categorical bigraphical model and the missing data problem are discussed.

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@inproceedings{Ning2013HighD, title={High - dimensional semiparametric bigraphical models}, author={Yang Ning and Han Liu}, year={2013} }