Two-Round Distributed Principal Component Analysis: Closing the Statistical Efficiency Gap

We enhance Fan et al.'s (2019) one-round distributed principal component analysis algorithm by adding a second fixed-point iteration round. Random matrix theory reveals the one-round estimator exhibits higher asymptotic error than the pooling estimator under moderate local signal-to-noise ratios. Remarkably, our second iteration round eliminates this efficiency gap. It follows from a careful analysis of the first-order perturbation of eigenspaces. Empirical experiments on synthetic and benchmark datasets consistently demonstrate the two-round method's statistical advantage over the one-round approach.