This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between potentially high-dimensional predictors and multiple responses, since it is known that Gaussian graphical models enable to exhibit direct links only, whereas coefficients in linear regressions contain both direct and indirect relations (due \textit{e.g.} to strong correlations among the variables). A smooth penalty reflecting a generalized Gaussian Bayesian prior on the covariates is added, either enforcing patterns (like row structures) in the direct links or regulating the joint influence of predictors. We give a theoretical guarantee for our method, taking the form of an upper bound on the estimation error arising with high probability, provided that the model is suitably regularized. Empirical studies on synthetic data and a real dataset are conducted.
翻译:本文专门用来估算带有结构上的贝叶西亚惩罚的局部图形模型。 确切地说,我们对通过潜在高维预测器和多个响应器之间的直接联系进行估计的线性回归环境感兴趣,因为众所周知,高西亚图形模型只能显示直接关联,而线性回归的系数包含直接和间接关系(应具有\ textit{e.g.} 与变量之间的密切关联)。 添加了一种平稳的处罚,反映了在共变中之前普遍存在的高山巴伊西亚人,无论是在直接链接中执行模式(如行结构),还是调节预测器的联合影响。 我们从理论上保证了我们的方法,采取高度概率估计错误的上限形式,前提是模型适当正规化。 进行了关于合成数据和真实数据集的实证研究。