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 real data set. KEYWORDS:
翻译:非正常图形模型是高斯图形模型对连续变量的半参数概括,在这种模型中,假设变量只有在经过一些未知的平滑单质变异之后,才遵循高斯图形模型。我们考虑在非正常图形模型中采用巴伊西亚法推论推理方法,在非正常图形模型中,我们通过基于 B-splines 的随机序列对未知变异进行前缀。我们使用回归公式来通过Cholesky对变异变量的精密矩阵进行分解来构建可能性,并在回归系数上加上缩进前缀。我们在模拟研究中采用插置变异巴伊西亚算法来学习稀薄精度矩阵,并将性能与远地点Gibbs取样方案进行比较。我们最终将拟议方法应用于一个真实的数据集。 KEYWORDS: