Complex-Valued Group Lasso For Tensor Autoregressive Models
I will introduce a group lasso algorithm for complex variables and demonstrate its application to a novel time series model called tensor autoregression (T-AR). T-AR utilizes the t-product tensor operation on 3-dimensional tensors and models time series exhibiting seasonality and geometric trend. The tensor structure of T-AR enables historical information from a selection of lag durations to simultaneously affect the prediction of a single series. I will first introduce the topic of tensor computations and motivate the t-product and T-SVD manipulations. Then, I will derive the T-AR model from the t-product definition and discuss its properties and interpretation. Next, I will adapt a group lasso algorithm to complex-valued problems and derive the fast algorithm for lag selection in T-AR. Finally, I will conclude with simulation results.
Van Loan,Charles Francis
M.S. of Statistics
Master of Science
dissertation or thesis