Universal Rank Inference via Residual Subsampling with Application to Large Networks

Understand

Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models.

• In this paper, 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.
• Our 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.