Restrict Outcomes for Estimation of Connectivity Matrix in Multi-layer Stochastic Block Fashions
Authors: Wenqing Su, Xiao Guo, Ying Yang
Summary: Multi-layer networks come up naturally in varied domains together with biology, finance and sociology, amongst others. The multi-layer stochastic block mannequin (multi-layer SBM) is often used for neighborhood detection within the multi-layer networks. Most of present literature focuses on statistical consistency of neighborhood detection strategies underneath multi-layer SBMs. Nevertheless, the asymptotic distributional properties are additionally indispensable which play an essential position in statistical inference. On this work, we goal to review the estimation and asymptotic properties of the layer-wise scaled connectivity matrices within the multi-layer SBMs. We develop a novel and environment friendly methodology to estimate the scaled connectivity matrices. Below the multi-layer SBM and its variant multi-layer degree-corrected SBM, we set up the asymptotic normality of the estimated matrices underneath delicate circumstances, which can be utilized for interval estimation and speculation testing. Simulations present the superior efficiency of proposed methodology over current strategies in two thought-about statistical inference duties. We additionally apply the strategy to an actual dataset and acquire interpretable outcomes.
