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2024-09-06
Fangzheng Xie, PhD, Department of Statistics, Indiana University
"Bias-corrected joint spectral embedding for multilayer networks with invariant subspace"
In this talk, I will introduce a novel bias-corrected joint spectral embedding algorithm to estimate the invariant subspace across heterogeneous multiple networks. The proposed algorithm recursively calibrates the diagonal bias of the sum of squared network adjacency matrices by leveraging the closed-form bias formula and iteratively updates the subspace estimator using the most recent estimated bias. Correspondingly, we establish a complete recipe for the entrywise subspace estimation theory for the proposed algorithm, including a sharp entrywise subspace perturbation bound and the entrywise eigenvector central limit theorem. Leveraging these results, we settle two multiple network inference problems: the exact community detection in multilayer stochastic block models and the hypothesis testing of the equality of membership profiles in multilayer mixed membership models.
