论文标题
极度稀疏网络的一般成对比较模型
A General Pairwise Comparison Model for Extremely Sparse Networks
论文作者
论文摘要
使用成对比较数据的统计推断是分析大规模稀疏网络的有效方法。在本文中，我们提出了一个通用框架，以模拟网络中的相互作用，该框架在模型参数化方面具有足够的灵活性。在此设置下，我们表明，在网络稀疏性的接近最小情况下，受试者潜在分数向量的最大似然估计量均匀地保持一致。就描述稀疏性的领先顺序渐近学而言，这种情况是鲜明的。我们的分析利用了一种新颖的链接技术，并说明了图形拓扑与模型一致性之间的重要联系。我们的结果确保最大似然估计器在数据渐近缺陷的大规模成对比较网络中是合理的。提供了模拟研究以支持我们的理论发现。
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample flexibility in terms of model parametrization. Under this setup, we show that the maximum likelihood estimator for the latent score vector of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This condition is sharp in terms of the leading order asymptotics describing the sparsity. Our analysis utilizes a novel chaining technique and illustrates an important connection between graph topology and model consistency. Our results guarantee that the maximum likelihood estimator is justified for estimation in large-scale pairwise comparison networks where data are asymptotically deficient. Simulation studies are provided in support of our theoretical findings.
