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Abstract:
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The degree-corrected mixed membership (DCMM) model is often used to model large social networks that have latent community structures and severe degree heterogeneity. We study the minimax rate for estimating the mixed membership vectors of individual nodes. The minimax rate depends on the degree parameters in a subtle way. To get a sharp lower bound, we carefully design the least-favorable configurations to reflect the role of degree parameters. To get a sharp upper bound, we propose a new spectral method and analyze it with a sharp entry-wise large-deviation bound for eigenvectors of the graph Laplacian. (Joint work with Jingming Wang).
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