Optimal rates for community estimation in the weighted stochastic block model
加权随机区块模型中社群估计的最优速率AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究加权网络中的社群识别与边权信息，符合网络方向，但并未涉及因果干扰效应。
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加权随机区块模型中社群估计的最优速率
- 研究问题
- 网络边权包含社群信息但其分布未知时，如何刻画社群误分的最优速率，并构造无需已知边权密度的可计算方法？
- 方法与思路
- 作者研究边权独立且密度由端点社群决定的加权区块模型，以社群内外边权分布的二分之一阶 Rényi 散度刻画误分率。
- 材料陈述的贡献
- 摘要称推广无权网络的最优误分率结果，并提出达到该速率的离散化算法；其适应性体现为无需预先知道边权密度。
- 阅读关注点
- 应核对社群规模与密度正则条件、误分损失和最优性的定义，以及离散化步骤如何兼顾计算可行性与未知密度适应性。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；最优性结论属于指定加权区块模型，摘要未说明依赖边或其他网络结构的适用性。
原文摘要
Community identification in a network is an important problem in fields such as social science, neuroscience and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this problem. However, SBMs have an important limitation in that they are suited only for networks with unweighted edges; in various scientific applications, disregarding the edge weights may result in a loss of valuable information. We study a weighted generalization of the SBM, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints. We characterize the optimal rate of misclustering error of the weighted SBM in terms of the Renyi divergence of order 1/2 between the weight distributions of within-community and between-community edges, substantially generalizing existing results for unweighted SBMs. Furthermore, we present a computationally tractable algorithm based on discretization that achieves the optimal error rate. Our method is adaptive in the sense that the algorithm, without assuming knowledge of the weight densities, performs as well as the best algorithm that knows the weight densities.