Correlation matrices are widely used to analyze the interdependence of variables in various real-world scenarios. Often, a perturbation in a few variables leads to mild differences in many correlation coefficients associated with these variables. We propose an efficient low-dimensional model that characterizes these differences as a product of single-variable effects. We develop methods for point estimation, confidence intervals, and hypothesis testing for this model. Importantly, our methods can account for both the variability in individual correlation matrices and for within-group variability. In simulations, our model shows increased power compared to competing approaches. We use the model to analyze resting-state functional MRI correlation matrices in patients with transient global amnesia and healthy controls. Our model detects significant decreases in synchronization for the patient population in several brain regions, which could not have been detected using previous methods without prior knowledge. Our methods are available in the open-source package \emph{github.com/itamarfaran/corrpops}.

翻译：相关矩阵被广泛用于分析各种现实场景中变量的相互依赖性。通常，少数变量的扰动会导致这些变量相关的多个相关系数出现轻微差异。我们提出了一种高效的低维模型，将这些差异表征为单变量效应的乘积。我们针对该模型开发了点估计、置信区间及假设检验方法。重要的是，我们的方法能够同时考虑个体相关矩阵的变异性和组内变异性。在模拟实验中，我们的模型相比竞争方法显示出更高的统计功效。我们利用该模型分析了短暂性全面遗忘症患者与健康对照组的静息态功能磁共振成像相关矩阵。我们的模型检测到患者群体在多个脑区的同步性显著降低——这种变化在缺乏先验知识的情况下无法通过以往方法检测到。相关方法已开源发布于 \emph{github.com/itamarfaran/corrpops}。