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Correlation matrices are widely used to analyze the interdependence ofvariables in various real-world scenarios. Often, a perturbation in a fewvariables leads to mild differences in many correlation coefficients associatedwith these variables. We propose an efficient low-dimensional model thatcharacterizes these differences as a product of single-variable effects. Wedevelop methods for point estimation, confidence intervals, and hypothesistesting for this model. Importantly, our methods can account for both thevariability in individual correlation matrices and for within-groupvariability. In simulations, our model shows increased power compared tocompeting approaches. We use the model to analyze resting-state functional MRIcorrelation matrices in patients with transient global amnesia and healthycontrols. Our model detects significant decreases in synchronization for thepatient population in several brain regions, which could not have been detectedusing previous methods without prior knowledge. Our methods are available inthe open-source package \emph{github.com/itamarfaran/corrpops}.

Detecting Differences Between Correlation-Matrix Populations due to Single-variable Perturbations, with Application to Resting State fMRI