A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations. We consider a Bayesian approach to inference in a nonparanormal graphical model in which we put priors on the unknown transformations through a random series based on B-splines. We use a regression formulation to construct the likelihood through the Cholesky decomposition on the underlying precision matrix of the transformed variables and put shrinkage priors on the regression coefficients. We apply a plug-in variational Bayesian algorithm for learning the sparse precision matrix and compare the performance to a posterior Gibbs sampling scheme in a simulation study. We finally apply the proposed methods to a microarray dataset. The proposed methods have better performance as the dimension increases, and in particular, the variational Bayesian approach has the potential to speed up the estimation in the Bayesian nonparanormal graphical model without the Gaussianity assumption while retaining the information to construct the graph.

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非超自然图模型的基于回归的贝叶斯估计和结构学习

非超常图模型是对连续变量的高斯图模型的半参数推广，其中假设变量仅在一些未知的平滑单调变换之后才遵循高斯图模型。我们考虑在非超自然图形模型中使用贝叶斯方法进行推理，在该模型中，我们通过基于 B 样条的随机序列对未知变换进行先验。我们使用回归公式通过对转换变量的基础精度矩阵进行 Cholesky 分解来构建似然性，并将收缩先验放在回归系数上。我们应用插件变分贝叶斯算法来学习稀疏精度矩阵，并将性能与模拟研究中的后验吉布斯采样方案进行比较。我们最终将所提出的方法应用于微阵列数据集。随着维度的增加，所提出的方法具有更好的性能，特别是变分贝叶斯方法有可能在没有高斯假设的情况下加速贝叶斯非超自然图模型中的估计，同时保留构建图的信息。