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With the rapid growth of neuroimaging technologies, a great effort has beendedicated recently to investigate the dynamic changes in brain activity.Examples include time course calcium imaging and dynamic brain functionalconnectivity. In this paper, we propose a novel nonparametric matrix responseregression model to characterize the nonlinear association between 2D imageoutcomes and predictors such as time and patient information. Our estimationprocedure can be formulated as a nuclear norm regularization problem, which cancapture the underlying low-rank structure of the dynamic 2D images. We presenta computationally efficient algorithm, derive the asymptotic theory and showthat the method outperforms other existing approaches in simulations. We thenapply the proposed method to a calcium imaging study for estimating the changeof fluorescent intensities of neurons, and an electroencephalography study fora comparison in the dynamic connectivity covariance matrices between alcoholicand control individuals. For both studies, the method leads to a substantialimprovement in prediction error.

Nonparametric Matrix Response Regression with Application to Brain Imaging Data Analysis