Post-Processing Posteriors Over Precision Matrices to Produce Sparse Graph Estimates
Post-Processing Posteriors Over Precision Matrices to Produce Sparse Graph Estimates
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DOI：
10.1214/18-ba1139
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发表时间：
2019-12-01
影响因子：
4.4
通讯作者：
Jones, M. Beatrix
中科院分区：
文献类型：
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作者：
Bashir, Amir;Carvalho, Carlos M.;Jones, M. Beatrix
多种计算效率高的贝叶斯模型的协方差矩阵的多元高斯分布是可用的。然而，所有这些方法都会产生相对密集的精度矩阵估计，因此，当人们希望使用精度矩阵来考虑数据的条件无关结构时，这些方法并不令人满意。本文考虑了这些协方差模型的模型拟合后验预测分布。然后，我们对精度矩阵的贝叶斯点估计进行后处理，以产生一个稀疏模型，其期望拟合位于拟合后验预测分布的95%以上。评价了选用精度矩阵零元方法的影响。使用鼓励稀疏后验（G-Wishart，贝叶斯自适应图形套索）和使用可信区间选择的模型获得了良好的结果。我们还发现，这种方法很容易扩展到寻找在一组精度矩阵上不同的元素的稀疏集的问题，这是在多个条件下观察到一组公共变量时的自然总结。我们用来自金融和代谢组学的中等维度数据示例来说明我们的发现。
A variety of computationally efficient Bayesian models for the covariance matrix of a multivariate Gaussian distribution are available. However, all produce a relatively dense estimate of the precision matrix, and are therefore unsatisfactory when one wishes to use the precision matrix to consider the conditional independence structure of the data. This paper considers the posterior predictive distribution of model fit for these covariance models. We then undertake post-processing of the Bayes point estimate for the precision matrix to produce a sparse model whose expected fit lies within the upper 95% of the posterior predictive distribution of fit. The impact of the method for selecting the zero elements of the precision matrix is evaluated. Good results were obtained using models that encouraged a sparse posterior (G-Wishart, Bayesian adaptive graphical lasso) and selection using credible intervals. We also find that this approach is easily extended to the problem of finding a sparse set of elements that differ across a set of precision matrices, a natural summary when a common set of variables is observed under multiple conditions. We illustrate our findings with moderate dimensional data examples from finance and metabolomics.