  Because tensor data appear more and more frequently in various scientific
researches and real-world applications, analyzing the relationship between
tensor features and the univariate outcome becomes an elementary task in many
fields. To solve this task, we propose \underline{Fa}st \underline{S}parse
\underline{T}ensor \underline{R}egression model (FasTR) based on so-called
unit-rank CANDECOMP/PARAFAC decomposition. FasTR first decomposes the tensor
coefficient into component vectors and then estimates each vector with $\ell_1$
regularized regression. Because of the independence of component vectors, FasTR
is able to solve in a parallel way and the time complexity is proved to be
superior to previous models. We evaluate the performance of FasTR on several
simulated datasets and a real-world fMRI dataset. Experiment results show that,
compared with four baseline models, in every case, FasTR can compute a better
solution within less time.
