发表机构
Research Institute for Statistics and Information Science, GSEM; University of Geneva（统计与信息科学研究所以及GSEM; 日内瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于图拉普拉斯近似推断的灵活潜变量模型，用于多视图网络数据降维，在理论和实证上优于传统泊松伪最大似然估计。
AI 中文摘要
我们提出了一种新颖且灵活的非线性方法，用于大规模多视图网络数据的降维，并推导了其理论。该（线性）预测器包含观测协变量（边特定、层特定和全局）以及高斯潜因子。推断通过图拉普拉斯近似最大似然估计器进行。令$K$表示网络层数，$n_V$表示节点数，我们在两种机制下推导渐近理论：（i）$K \to \infty$且$n_V$固定，（ii）双重渐近$K, n_V \to \infty$，为局部和全局参数建立一致性和渐近正态性，并具有不同的收敛速率。在商品贸易的引力模型应用中，我们使用零调整伽马分布，包含潜因子和可观测协变量（如距离、关税、共同语言），以捕捉过量零值、偏度和未观测异质性。合成和真实数据实验表明，我们的方法优于常规应用的带固定效应的泊松伪最大似然估计器。我们通过开源R/C++例程和一种新颖的起始值选择策略，补充了理论和实证贡献。
英文摘要
We propose a novel and flexible nonlinear approach for dimensionality reduction of large-scale multiview network data and derive its theory. The (linear) predictor incorporates observed covariates (edge-specific, layer-specific, and global) and Gaussian latent factors. Inference is conducted via the graph Laplace approximated maximum likelihood estimator. Letting $K$ denote the number of network layers and $n_V$ the number of nodes, we derive asymptotic theory under two regimes: (i) $K \to \infty$ with fixed $n_V$, and (ii) double asymptotics $K, n_V \to \infty$, establishing consistency and asymptotic normality for local and global parameters, with distinct convergence rates. In an application to the gravity model for commodity trades, we use a zero-adjusted Gamma distribution with latent factors and observable covariates (e.g.\ distance, tariffs, common language) to capture excess zeros, skewness, and unobserved heterogeneity. Synthetic and real-data exercises show that our approach outperforms the routinely applied Poisson pseudo-maximum likelihood estimator with fixed effects. We complement our theoretical and empirical contributions with open-source R/C++ routines and a novel strategy for starting values selection.
