Fast and Scalable Estimator for Sparse and Unit-Rank Higher-Order Regression Models
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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 Fast Sparse Tensor Regression 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 ℓ_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.
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