A1266
Title: Tensor-on-tensor time series regression
Authors: Ranjan Maitra - Iowa State University (United States) [presenting]
Subrata Pal - Washington University (United States)
Abstract: Data acquisition in a functional Magnetic Resonance Imaging (fMRI) activation detection experiment yields a massively structured array- or tensor-variate dataset that needs to be analyzed with respect to a set of time-varying stimuli and possibly other covariates. The conventional approach employs a two-stage analysis: The first stage fits univariate regression on The time series data at each individual voxel and reduces The voxel-wise data to a single statistic. The statistical parametric map formed from these voxel-wise test statistics is then fed into a second-stage analysis that potentially incorporates spatial context between The voxels and identifies activation within them. A holistic yet practical tensor-variate methodology provides one-stage tensor-variate regression modeling of The entire time series array-variate dataset. Low-rank specifications on The tensor-variate regression parameters and Kronecker separable error covariance tensors make this approach feasible. A block relaxation algorithm provides maximum likelihood estimates of The model parameters. The methods are implemented via an R package that incorporates numerous computational simplifications for efficiency and scalability. Performance on realistic simulation studies and a functional MRI study about Major Depressive Disorder demonstrates The stability of The approach and that it can reliably identify cerebral regions that are significantly activated.
