A0690
Title: Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA
Authors: Runbing Zheng - Johns Hopkins University (United States) [presenting]
Minh Tang - North Carolina State University (United States)
Abstract: The problem of distributed estimation of the leading singular vectors is studied for a collection of matrices with shared invariant subspaces. In particular, an algorithm is considered that first estimates the projection matrices corresponding to the leading singular vectors for each individual matrix, then computes the average of the projection matrices, and finally returns the leading eigenvectors of the sample averages. It is shown that the algorithm, when applied to (1) parameters estimation for a collection of independent edge random graphs with shared singular vectors but possibly heterogeneous edge probabilities or (2) distributed PCA for independent sub-Gaussian random vectors with spiked covariance structure, yields estimates whose row-wise fluctuations are normally distributed around the rows of the true singular vectors. Leveraging these results, a two-sample test is also considered for the null hypothesis that a pair of random graphs have the same edge probabilities, and a test statistic is presented whose limiting distribution converges to a central (resp. non-central) $\chi^2$ under the null (resp. local alternative) hypothesis.
