Statistics Department Seminar Series: Ziwei Zhu, Department of Operations Research and Financial Engineering, Princeton University

Modern data sets are often decentralized; they are generated and stored in multiple sources across which the communication is constrained by bandwidth or privacy. This talk focuses on distributed estimation of principal eigenspaces of covariance matrices with decentralized data. We introduce and analyze a distributed algorithm that aggregates multiple principal eigenspaces through averaging the corresponding projection matrices. When the data distribution has sign-symmetric innovation, the distributed PCA is proved to be “unbiased” such that its statistical error will converge to zero as the number of data splits grows to infinity. For general distributions, when the number of data splits is not large, this algorithm is shown to achieve the same statistical efficiency as the full sample oracle. We applied our algorithm to implement distributed partition of traffic network of Manhattan; the distributed procedure delivered similar partition results as the centralized procedure provided that the number of data splits is not large.