The recovery of the causality networks with a number of variables is an important problem that arises in various scientific contexts. For detecting the causal relationships between variables in the network, the concept of the so called multivariate Granger causality has been proposed. Its application to the networks with a big number of variables requires a variable selection procedure. The Lasso is a well known example of such a procedure, and the method for reconstructing causality networks using the multivariate Granger causality with the Lasso is called Graphical Lasso Granger (GLG) method. It is widely believed that the GLG-method tends to overselect causal relationships. In this paper, we propose a thresholding strategy for the GLG-method, which we call 2-levels-thresholding, and we show that with this strategy the variable overselection of the GLG-method may be overcomed. Moreover, we demonstrate that the GLG-method with the proposed thresholding strategy may become superior to other methods that were proposed for the recovery of the causality networks.

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