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Title: High dimensional tensor regression for neuroimaging data Authors:  Montserrat Fuentes - Virginia Commonwealth University (United States) [presenting]
Abstract: Imaging data with thousands of spatially-correlated data points are common in many fields. In Neurosciences, magnetic resonance imaging (MRI) is essential for studying brain structure and activity. Modeling spatial dependence of MRI data at different scales is key. It could allow for accurate testing for significance in neural activity. The high dimensionality presents modeling and computational challenges. Methods that account for spatial correlation often require cumbersome matrix evaluations which are prohibitive for large data. Thus, current methods typically reduce dimensionality by modeling covariance among regions of interest coarser or larger spatial units rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect activation patterns in the brain, and hence produce misleading results. We introduce a novel Bayesian Tensor approach, treating the brain image as response and having a vector of predictors. Parameter estimates using a generalized sparsity principle are provided. A fully Bayesian approach to characterize different sources of uncertainty is employed. We demonstrate posterior consistency and develop a computationally efficient algorithm. The effectiveness is illustrated through simulations and the analysis of the effects of cocaine addiction on the brain structure. The aim is to identify the effects of demographic information and cocaine addiction on the functioning of the brain.