快速贝叶斯高维高斯图模型估计
Fast Bayesian High-Dimensional Gaussian Graphical Model Estimation
AI总结：
本文提出一种基于贝叶斯邻域回归集成的高维高斯图模型估计方法，利用Horseshoe先验和基于边际似然的变量选择实现稀疏性与并行化，并通过模拟及三阴性乳腺癌基因表达数据验证其性能。
摘要：
图模型通过条件独立的概念描述变量之间的关联。高斯图模型是一类广泛使用的此类模型，其中关系由精度矩阵的非零项形式化表示。然而，在高维情形下，标准协方差估计通常不稳定。此外，在许多现实应用中，自然预期只存在少数显著关联。这需要在估计中引入稀疏性技术。经典频率学派方法为此使用惩罚；相比之下，完全贝叶斯方法计算速度慢，通常需要在受正定性约束的空间中对二次方数量的参数进行迭代采样。我们提出一种基于贝叶斯邻域回归集成的贝叶斯图估计方法。我们的方法的一个有吸引力的特点是能够跨不同的图邻域轻松并行化，从而获得比大多数现有方法更高的计算效率。我们的策略通过Horseshoe收缩先验引入稀疏性，并包含一个基于预测变量秩的边际似然的新变量选择步骤。我们的方法适当地结合估计的回归系数，以产生图估计和用于推断的偏相关估计矩阵。使用FDR和TPR等指标评估各种方法的性能。通过大量模拟展示了在各种情况下的竞争性能。最后，我们应用这些方法研究三阴性乳腺癌女性基因表达之间的依赖结构。
英文摘要：
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the precision matrix. However, in high dimensional cases, standard covariance estimates are typically unstable. Moreover, it is natural to expect only a few significant associations to be present in many realistic applications. This necessitates the injection of sparsity techniques into the estimation. Classical frequentist methods use penalization for this purpose; in contrast, fully Bayesian methods are computationally slow, typically requiring iterative sampling over a quadratic number of parameters in a space constrained by positive definiteness. We propose a Bayesian graph estimation method based on an ensemble of Bayesian neighborhood regressions. An attractive feature of our methods is the ability for easy parallelization across separate graphical neighborhoods, invoking computational efficiency greater than most existing methods. Our strategy induces sparsity with a Horseshoe shrinkage prior and includes a novel variable selection step based on the marginal likelihood from the predictors ranks. Our method appropriately combines the estimated regression coefficients to produce a graph estimate and a matrix of partial correlation estimates for inference. Performance of various methods are assessed using measures like FDR and TPR. Competitive performance across a variety of cases is demonstrated through extensive simulations. Lastly, we apply these methods to investigate the dependence structure across genetic expressions for women with triple negative breast cancer.
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