Spectral feature selection with the graphical lasso estimator for ultra-high dimensional Gaussian graphical models

Rui Chen, Erbo Li, Yushan Xue, Yuehan Yang

Abstract: High-dimensional sparse Gaussian graphical modeling often suffers from the dimensionality of the parameter space and computational complexity. Inspired by the computational advantage of the filter modeling, we propose a novel two-step method, named Spectral feature selection with the graphical lasso (SPECfs-Glasso). This method first builds the filter modeling for dimension reduction. We use the spectral analysis, Spectral Feature Selection (SPECfs)35, to study the graph structure. In the first step, many “irrelevant” variables are removed from further consideration. The dimension of the parameter space is effectively reduced. We then estimate the sparse concentration matrix by the graphical lasso in the shrunk space, obtaining an accurate estimation with a low computational cost. We have shown that the proposed method has theoretical guarantees. In the numerical simulation, comparisons between our method and some existing methods indicate that our method has good performance. The computational time of the algorithm is significantly lower than the others. We analyze a breast cancer microarray data set with our proposed method and gain some interesting and meaningful results in the biological field.