Power Iteration for Tensor PCA

Understand

In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44].

• We give necessary and sufficient conditions for the convergence of the power iteration algorithm.
• When the power iteration algorithm converges, for the rank one spiked tensor model, we show the estimators for the spike strength and linear functionals of the signal are asymptotically Gaussian; for the multi-rank spiked tensor model, we show the estimators are asymptotically mixtures of Gaussian.
• This new phenomenon is different from the spiked matrix model.