Revealing Common Statistical Behaviors in Heterogeneous Populations

In many areas of neuroscience and biological data analysis, it is desired to reveal common patterns among a group of subjects. Such analyses play important roles e.g., in detecting functional brain networks from fMRI scans and in identifying brain regions which show increased activity in response to certain stimuli. Group level techniques usually assume that all subjects in the group behave according to a single statistical model, or that deviations from the common model have simple parametric forms. Therefore, complex subject-specific deviations from the common model severely impair the performance of such methods. In this paper, we propose nonparametric algorithms for estimating the common covariance matrix and the common density function of several variables in a heterogeneous group of subjects. Our estimates converge to the true model as the number of subjects tends to infinity, under very mild conditions. We illustrate the effectiveness of our methods through extensive simulations as well as on real-data from fMRI scans and from arterial blood pressure and photoplethysmogram measurements.