Abstract A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open problem is how to estimate such models from large networks. A novel approach to large-scale estimation is proposed, taking advantage of the local structure of such models for the purpose of local computing. The main idea is that random graphs with local dependence can be decomposed into subgraphs, which enables parallel computing on subgraphs and suggests a two-step estimation approach. The first step estimates the local structure underlying random graphs. The second step estimates parameters given the estimated local structure of random graphs. Both steps can be implemented in parallel, which enables large-scale estimation. The advantages of the two-step estimation approach are demonstrated by simulation studies with up to 10,000 nodes and an application to a large Amazon product recommendation network with more than 10,000 products.

中文翻译：

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具有局部依赖性的随机图模型的大规模估计

摘要 考虑一类随机图模型，结合指数族模型和潜在结构模型的特征，目标是保留两者的优点，同时减少各自的缺点。一个悬而未决的问题是如何从大型网络中估计此类模型。提出了一种大规模估计的新方法，利用此类模型的局部结构进行局部计算。主要思想是具有局部依赖性的随机图可以分解为子图，从而可以对子图进行并行计算，并提出了一种两步估计方法。第一步估计随机图的局部结构。第二步在给定随机图的估计局部结构的情况下估计参数。这两个步骤可以并行实施，从而实现大规模估计。两步估计方法的优点通过最多 10,000 个节点的模拟研究以及在包含 10,000 多种产品的大型亚马逊产品推荐网络中的应用得到了证明。