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Abstract:
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Multimodal data are now prevailing in scientific research. A central question in multimodal integrative analysis is to understand how two data modalities associate and interact with each other given another modality or demographic covariates. The problem can be formulated as studying the associations among three sets of random variables, a question that has received relatively less attention in the literature. In this talk, we discuss new models and methods for studying three-way associations. We establish population dimension reduction models, connecting the problem to Tucker decomposition of a three-way tensor and regression of a correlation matrix. We demonstrate the efficacy of the methods through both simulations and multimodal neuroimaging applications.
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