Nonparametric Matrix Response Regression with Application to Brain Imaging Data Analysis
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With the rapid growth of neuroimaging technologies, a great effort has been dedicated recently to investigate the dynamic changes in brain activity. Examples include time course calcium imaging and dynamic brain functional connectivity. In this paper, we propose a novel nonparametric matrix response regression model to characterize the association between 2D image outcomes and predictors such as time and patient information. Our estimation procedure can be formulated as a nuclear norm regularization problem, which can capture the underlying low-rank structures of the dynamic 2D images. We develop an efficient algorithm to solve the optimization problem and introduce a Bayesian information criterion for our model to select the tuning parameters. Asymptotic theories including the risk bound and rank consistency are derived. We finally evaluate the empirical performance of our method using numerical simulations and real data applications from a calcium imaging study and an electroencephalography study.
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