A0744
Title: Spiked tensor model
Authors: Jiaoyang Huang - University of Pennsylvania (United States) [presenting]
Abstract: The spiked tensor model is discussed, where one needs to extract information from a noisy high-dimensional data tensor. The algorithmic aspect of this model will be considered. First, the tensor power iteration algorithm will be considered, a natural generalization of the matrix power iteration. Necessary and sufficient conditions for the convergence of the power iteration algorithm are given. When the power iteration algorithm converges, for the rank one spiked tensor model, it is shown that the estimators for the spike strength and linear functionals of the signal are asymptotically Gaussian; for the multi-rank spiked tensor model, it is shown that the estimators are asymptotically mixtures of Gaussian. This new phenomenon is different from the spiked matrix model. Second, the tensor unfolding algorithm will be discussed. It results in a spiked random matrix where the number of rows (columns) grows polynomially in the number of columns (rows). By analyzing its spectrum, an exact threshold is obtained for the tensor unfolding algorithm, which is independent of the unfolding procedure. This threshold matches the conjectured computational threshold of the spiked tensor model.
