Few-Round Distributed Principal Component Analysis: Closing the Statistical Efficiency Gap by Consensus
提出一种少轮次共识的移位子空间迭代算法，改进分布式主成分分析，在弱信噪比下缩小局部相变差距、降低渐近方差并减少偏差，适用于重尾数据的分布式椭圆PCA。
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit of divide-and-conquer by introducing a few additional communication rounds of consensus. The proposed shifted subspace iteration algorithm is able to close the local phase transition gap, reduce the asymptotic variance, and alleviate potential bias. Our estimation procedure is easy to implement and tuning-free. The resulting estimator is shown to be statistically efficient after an acceptable number of iterations. We also discuss extensions to distributed elliptical PCA for heavy-tailed data. Empirical experiments on synthetic and benchmark datasets demonstrate our method’s statistical advantage over the divide-and-conquer approach.