论文标题
在预测因子和响应之间的直接链接上具有结构性先验的部分图形模型
A partial graphical model with a structural prior on the direct links between predictors and responses
论文作者
论文摘要
本文致力于估计具有结构性贝叶斯惩罚的部分图形模型。 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).添加了反映广义高斯贝叶斯在协变量上的平稳惩罚，要么在直接链接中强制执行模式（例如行结构），要么调节预测变量的关节影响。我们为我们的方法提供了理论保证，以高可能性产生的估计误差的上限形式，只要模型是适当正规化的。进行了关于合成数据和实际数据集的经验研究。
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.
