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Bickel 等对《Varimax 经典因子分析实现统计推断》的讨论意见AI 解读

We compliment the authors for their unification of old and new latent variable models. Their motivation seems to have come from Thurstone’s Factor Analysis and the wish to explain the somewhat mysterious success of Kaiser’s Varimax rule in that context. However, their major applications and notation stem from overlapping network community detection and Latent Dirichlet Allocation (LDA) (Blei et al., 2003). Inference for these models can be unified in another way via a…

最小假设下稀疏图子的子抽样AI 解读

Summary We study the properties of two subsampling procedures for networks, vertex subsampling and $p$-subsampling, under the sparse graphon model. The consistency of network subsampling is demonstrated under the minimal assumptions of weak convergence of the corresponding network statistics and an expected subsample size growing to infinity more slowly than the number of vertices in the network. Furthermore, under appropriate sparsity conditions, we derive limiting…

稀疏图中协变量正则化的社区发现AI 解读

In this article, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full cluster structure by considering both. In statistics, an emerging body of work has been focused on combining information from both the edges in the network and the node covariates to infer community memberships. However, so far the…

用于网络自动社群发现的假设检验AI 解读

Summary Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of finding communities or clusters in a network has received much attention from statistics, physics and computer science. However, most clustering algorithms assume knowledge of the number of clusters k. We propose to determine k…

面向海量数据的可扩展自助法AI 解读

Summary The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large data sets—which are increasingly prevalent—the calculation of bootstrap-based quantities can be prohibitively demanding computationally. Although variants such as subsampling and the m out of n bootstrap can be used in principle to reduce the cost of bootstrap computations, these methods are generally not robust to specification of tuning…