Minimax rates of community detection in stochastic block models
随机块模型社区检测的极小极大速率AI 解读 ↓
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随机块模型社区检测的极小极大速率
- 研究问题
- 随机块模型下社区识别的错配比例能达到怎样的极小极大速率，网络稀疏性与社区数量如何关联精确和部分恢复？
- 方法与思路
- 作者以惩罚似然类方法建立上界，并利用可交换性将全局错配问题化为单节点的局部聚类问题，构造相应下界。
- 材料陈述的贡献
- 摘要称获得覆盖多类随机块模型的指数型极小极大速率，并据此建立精确恢复与部分恢复的一致性阈值现象。
- 阅读关注点
- 应核对各模型参数空间、错配损失的定义及社区标签处理，查看上下界适用条件和惩罚似然方法的计算要求。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明；具体速率表达式、阈值条件及算法可行性未说明，不能推断刊本变化。
原文摘要
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 minimax rates of the mis-match ratio for a wide rage of settings including homogeneous and inhomogeneous SBMs, dense and sparse networks, finite and growing number of communities. The minimax rates are exponential, different from polynomial rates we often see in statistical literature. An immediate consequence of the result is to establish threshold phenomenon for strong consistency (exact recovery) as well as weak consistency (partial recovery). We obtain the upper bound by a range of penalized likelihood-type approaches. The lower bound is achieved by a novel reduction from a global mis-match ratio to a local clustering problem for one node through an exchangeability property.