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Abstract:
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Functional graphical modeling is gaining increasing attention in recent years, where the central goal is to investigate the interdependency among multivariate random functions. In this talk, we consider two case studies. The first one models the functional graphical model conditioning on external variables such as time or additional covariates. The second one studies the functional structural equation model. Both studies are built upon linear operators developed in some reproducing kernel Hilbert space. We derive the estimators at both the operator level and under a coordinate system. We establish the theoretical guarantees, and illustrate the methods with some neuroimaging applications.
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