The functional and structural representation of the brain as a complex
network is marked by the fact that the comparison of noisy and intrinsically
correlated high-dimensional structures between experimental conditions or
groups shuns typical mass univariate methods. Furthermore most network
estimation methods cannot distinguish between real and spurious correlation
arising from the convolution due to nodes' interaction, which thus introduces
additional noise in the data. We propose a machine learning pipeline aimed at
identifying multivariate differences between brain networks associated to
different experimental conditions. The pipeline (1) leverages the deconvolved
individual contribution of each edge and (2) maps the task into a sparse
classification problem in order to construct the associated "sparse deconvolved
predictive network", i.e., a graph with the same nodes of those compared but
whose edge weights are defined by their relevance for out of sample predictions
in classification. We present an application of the proposed method by decoding
the covert attention direction (left or right) based on the single-trial
functional connectivity matrix extracted from high-frequency
magnetoencephalography (MEG) data. Our results demonstrate how network
deconvolution matched with sparse classification methods outperforms typical
approaches for MEG decoding