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社会网络平衡性检验AI 解读

Friendship and antipathy exist in concert with one another in real social networks. Despite the role they play in social interactions, antagonistic ties are poorly understood and infrequently measured. One important theory of negative ties that has received relatively little empirical evaluation is balance theory, the codification of the adage “the enemy of my enemy is my friend” and similar sayings. Unbalanced triangles are those with an odd number of negative ties, and the…

社群识别中均值场变分推断的理论与计算保证AI 解读

The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been…

度修正块模型中的社区检测AI 解读

Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown…

随机块模型社区检测的极小极大速率AI 解读

Recently, network analysis has gained more and more attention in statistics, as well as in computer science, probability and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic in network analysis. Many methodologies have been proposed. Some beautiful and significant phase transition results are obtained in various settings. In this paper, we provide a general minimax theory for community detection. It gives…

达到最优收敛率的 Graphon 估计AI 解读

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with $k$ clusters, we show that the optimal rate under the mean squared error is $n^{-1}\log k+k^{2}/n^{2}$…