基于谱分析的多元线性模型混杂检测
Detecting confounding in multivariate linear models via spectral analysis
摘要：
我们研究了一个模型，其中一个目标变量Y与向量X：=（X_1，...，X_d）是Y的潜在原因。我们描述了一种方法，该方法推断X和Y之间的统计依赖性在多大程度上是由于X对Y的影响，以及在多大程度上是由于X和Y的隐藏的共同原因（混杂因素）。该方法依赖于大维度d的测量结果的集中和独立性假设，即在不存在混杂的情况下，描述每个X对Y的影响的回归系数的向量相对于X的协方差阵的特征空间通常具有“通用方向”。对于一个标量混杂的特殊情况下，我们表明，混杂通常会破坏这种通用的方向在一个特征的方式，可以用来定量估计的混杂量。
英文摘要：
We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are due to the influence of X on Y and to what extent due to a hidden common cause (confounder) of X and Y. The method relies on concentration of measure results for large dimensions d and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of each X on Y typically has `generic orientation' relative to the eigenspaces of the covariance matrix of X. For the special case of a scalar confounder we show that confounding typically spoils this generic orientation in a characteristic way that can be used to quantitatively estimate the amount of confounding.
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