论文标题
基于伪样的$ m $估计随机图的依赖边缘和尺寸增加的参数向量
Pseudo-likelihood-based $M$-estimation of random graphs with dependent edges and parameter vectors of increasing dimension
论文作者
论文摘要
统计网络分析中的一个重要问题是如何估算具有棘手的似然函数的离散和依赖网络数据模型，而无需牺牲计算可扩展性和统计保证。我们证明，通过建立基于伪样的$ m $ m估计器的收敛速率，对于具有指数参数化的离散图形模型和增加单观景场景中增加维数的参数向量的离散图形模型的可扩展估计是可能的。我们强调了两种复杂现象对收敛速率的影响：相变和模型接近度。主要结果可能应用于离散和依赖网络，空间和时间数据。为了展示收敛速率，我们介绍了一类新型的广义$β$模型，具有依赖的边缘和尺寸增加的参数向量，这些尺寸增加了尺寸，以重叠亚群的形式利用额外的结构来控制依赖性。我们建立了基于伪样的$ m $ m $估计量的融合率，用于通用的$β$ - 模型，并在密集和稀疏式环境中。
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We demonstrate that scalable estimation of random graph models with dependent edges is possible, by establishing convergence rates of pseudo-likelihood-based $M$-estimators for discrete undirected graphical models with exponential parameterizations and parameter vectors of increasing dimension in single-observation scenarios. We highlight the impact of two complex phenomena on the convergence rate: phase transitions and model near-degeneracy. The main results have possible applications to discrete and dependent network, spatial, and temporal data. To showcase convergence rates, we introduce a novel class of generalized $β$-models with dependent edges and parameter vectors of increasing dimension, which leverage additional structure in the form of overlapping subpopulations to control dependence. We establish convergence rates of pseudo-likelihood-based $M$-estimators for generalized $β$-models in dense- and sparse-graph settings.
