56: Tensor Response Regression with Low Tubal Rank and Sparsity

Music City Center 

For contemporary scientific data, complicated structured tensor data with high dimensions are everywhere. Motivated by modeling the relationship between the multivariate covariates with the complicated tensor response, we proposed a tensor response model with low tubal rank and sparsity constraint. The low tubal rank constraint can capture the space-shifting or time-shifting characteristic of the data while sparsity can reduce the number of free parameters.

One special case of our model is equivalent to the multivariate reduced rank regression model. We also put forward a proven convergent ADMM algorithm that can obtain the optimized estimation efficiently. Simulations show that our method significantly outperforms the existing tensor response models.

ADMM

multidimensional array

multivariate linear regression

reduced rank regression

tubal rank

fourier transform 

Section on Statistical Learning and Data Science