B2002
Title: Distributed estimation of invariant subspaces in multiple network inference
Authors: Minh Tang - North Carolina State University (United States)
Runbing Zheng - Johns Hopkins University (United States) [presenting]
Abstract: The distributed estimation of invariant subspace for multiple networks is studied. For a collection of heterogeneous random graphs, we study the problem of estimating the common left and right singular subspaces, and analyze a distributed algorithm that first estimates the projection matrices corresponding to these subspaces for each individual graph, then computes the average of the projection matrices, and finally returns the leading eigenvectors of the sample averages. We show that the algorithm yields estimates whose row-wise fluctuations are normally distributed around the rows of the true singular vectors. We next consider a two-sample test for the null hypothesis that two graphs have the same edge probabilities matrices against the alternative hypothesis that their edge probabilities matrices are different, and we present a test statistic whose limiting distribution converges to a central Chi-squared (resp. non-central Chi-squared) under the null (resp. alternative) hypothesis. We also extend the theoretical analysis to other problems including distributed PCA.
