Li Bing, Chun Hyonho, Zhao Hongyu
Professor of Statistics, The Pennsylvania State University, 326 Thomas Building, University Park, PA 16802.
Assistant Professor of Statistics, Purdue University, 250 N. University Street, West Lafayette, IN 47907.
J Am Stat Assoc. 2014 Sep;109(507):1188-1204. doi: 10.1080/01621459.2014.882842.
We introduce a nonparametric method for estimating non-gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among random vectors that resembles the logical structure of conditional independence. Additive conditional independence allows us to use one-dimensional kernel regardless of the dimension of the graph, which not only avoids the curse of dimensionality but also simplifies computation. It also gives rise to a parallel structure to the gaussian graphical model that replaces the precision matrix by an additive precision operator. The estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case, but outperform it when the gaussian copula assumption is violated. We compare the new method with existing ones by simulations and in genetic pathway analysis.
我们基于一种称为加性条件独立性的新统计关系，引入了一种用于估计非高斯图形模型的非参数方法。加性条件独立性是随机向量之间的一种三元关系，类似于条件独立性的逻辑结构。加性条件独立性使我们能够使用一维核，而无需考虑图的维度，这不仅避免了维数灾难，还简化了计算。它还产生了一种与高斯图形模型并行的结构，该结构用加性精度算子代替了精度矩阵。从加性条件独立性导出的估计量涵盖了最近引入的非正态图形模型作为一种特殊情况，但在违反高斯copula假设时表现优于该模型。我们通过模拟和基因通路分析将新方法与现有方法进行了比较。
