Title: Universal rank inference via residual subsampling with application to large networks
Authors: Yingying Fan - University of Southern California (United States) [presenting]
Xiao Han - University of Science and Technology of China (China)
Qing Yang - USTC (China)
Abstract: Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. We suggest a universal approach to rank inference via residual subsampling (RIRS) for testing and estimating rank in a wide family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. The procedure constructs a test statistic via subsampling entries of the residual matrix after extracting the spiked components. The test statistic converges in distribution to the standard normal under the null hypothesis, and diverges to infinity with asymptotic probability one under the alternative hypothesis. The effectiveness of RIRS procedure is justified theoretically, utilizing asymptotic expansions of eigenvectors and eigenvalues for large random matrices recently developed. The advantages of the newly suggested procedure are demonstrated through several simulations and real data examples.