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This paper is devoted to the estimation of a partial graphical model with astructural Bayesian penalization. Precisely, we are interested in the linearregression setting where the estimation is made through the direct linksbetween potentially high-dimensional predictors and multiple responses, sinceit is known that Gaussian graphical models enable to exhibit direct links only,whereas coefficients in linear regressions contain both direct and indirectrelations (due \textit{e.g.} to strong correlations among the variables). Asmooth penalty reflecting a generalized Gaussian Bayesian prior on thecovariates is added, either enforcing patterns (like row structures) in thedirect links or regulating the joint influence of predictors. We give atheoretical guarantee for our method, taking the form of an upper bound on theestimation error arising with high probability, provided that the model issuitably regularized. Empirical studies on synthetic data and a real datasetare conducted.

A partial graphical model with a structural prior on the direct links between predictors and responses