We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying variables follow a multivariate Gaussian distribution, if no measurement error is present, this problem is often solved by estimating the precision matrix under sparsity constraints. However, when measurement error is present, not correcting for it leads to inconsistent estimates of the precision matrix and poor identification of relationships. We propose a new Bayesian methodology to correct for the measurement error from the observed samples. This Bayesian procedure utilizes a recent variant of the spike-and-slab Lasso to obtain a point estimate of the precision matrix, and corrects for the contamination via the recently proposed Imputation-Regularization Optimization procedure designed for missing data. Our method is shown to perform better than the naive method that ignores measurement error in both identification and estimation accuracy. To show the utility of the method, we apply the new method to establish a conditional gene network from a microarray dataset.

中文翻译：

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具有测量误差的高斯图模型的贝叶斯正则化

当观察到的样本在高维设置中受到测量误差的污染时，我们考虑了一个用于确定和估计变量的条件成对关系的框架。假设真正的底层变量遵循多元高斯分布，如果不存在测量误差，这个问题通常通过在稀疏约束下估计精度矩阵来解决。然而，当存在测量误差时，不对其进行校正会导致精度矩阵的估计不一致和关系识别不佳。我们提出了一种新的贝叶斯方法来纠正观察样本的测量误差。这个贝叶斯过程利用了尖刺和板套索的最新变体来获得精度矩阵的点估计，并通过最近提出的为缺失数据设计的插补-正则化优化程序来纠正污染。我们的方法被证明比在识别和估计精度方面忽略测量误差的朴素方法表现更好。为了展示该方法的实用性，我们应用新方法从微阵列数据集建立条件基因网络。