Gaussian graphical models are widely utilized to infer and visualize networksof dependencies between continuous variables. However, inferring the graph isdifficult when the sample size is small compared to the number of variables. Toreduce the number of parameters to estimate in the model, we propose anon-asymptotic model selection procedure supported by strong theoreticalguarantees based on an oracle inequality and a minimax lower bound. Thecovariance matrix of the model is approximated by a block-diagonal matrix. Thestructure of this matrix is detected by thresholding the sample covariancematrix, where the threshold is selected using the slope heuristic. Based on theblock-diagonal structure of the covariance matrix, the estimation problem isdivided into several independent problems: subsequently, the network ofdependencies between variables is inferred using the graphical lasso algorithmin each block. The performance of the procedure is illustrated on simulateddata. An application to a real gene expression dataset with a limited samplesize is also presented: the dimension reduction allows attention to beobjectively focused on interactions among smaller subsets of genes, leading toa more parsimonious and interpretable modular network.
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