In problems where a distribution is concentrated in a lower-dimensional subspace, the covariance matrix faces a singularity problem. In downstream statistical analyzes this can cause a problem as the inverse of the covariance matrix is often required in the likelihood. There are several methods to overcome this challenge. The most wellknown ones are the eigenvalue, singular value, and Cholesky decompositions. In this short note, we develop a new method to deal with the singularity problem while preserving the covariance structure of the original matrix. We compare our alternative with other methods. In a simulation study, we generate various covariance matrices that have different dimensions and dependency structures, and compare the CPU times of each approach.
Introduction:The Gaussian Graphical Model (GGM) is one of the well-known probabilistic models which is based on the conditional independency of nodes in the biological system. Here, we compare the estimates of the GGM parameters by the graphical lasso (glasso) method and the threshold gradient descent (TGD) algorithm.Methods:We evaluate the performance of both techniques via certain measures such as specificity, F-measure and AUC (area under the curve). The analyses are conducted by Monte Carlo runs under different dimensional systems.Results:The results indicate that the TGD algorithm is more accurate than the glasso method in all selected criteria, whereas, it is more computationally demanding than this method too.Discussion and conclusion:Therefore, in high dimensional systems, we recommend glasso for its computational efficiency in spite of its loss in accuracy and we believe than the computational cost of the TGD algorithm can be improved by suggesting alternative steps in inference of the network.
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