Establish guarantees for the initialization threshold in streaming truncated power under spiked models

Establish a theoretical guarantee that the initialization procedure of Yang and Xu (2015)—which uses a streaming PCA algorithm until reaching a specified accuracy threshold—indeed achieves the required threshold in the spiked high-dimensional covariance model setting.

Background

The paper surveys prior streaming sparse PCA algorithms, noting that some methods (e.g., an online block version of the truncated power method) rely on an initialization that must meet a prescribed accuracy level. The authors point out that, for the spiked high-dimensional setting, there is no theoretical guarantee that this initialization procedure reaches the required threshold.

Providing such a guarantee would clarify the applicability of the truncated power method initialization in high-dimensional regimes and strengthen theoretical foundations of streaming sparse PCA methods in the spiked covariance model.