[论文解读] A Bayesian Dynamic Latent Space Model for Weighted Networks

Roberto Casarin, Matteo Iacopini+1 more|arXiv (Cornell University)|Mar 25, 2026

Mental Health Research Topics被引用 0

一句话总结

引入一个用于计数值加权网络且含有零膨胀的贝叶斯动态潜在空间特征矩阵模型（eigenmodel），实现时间变化的节点特征与稀疏性；采用辅助混合数据增广和部分坍缩吉布斯采样，有效推断潜在空间维度及轨迹。

ABSTRACT

A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent positions evolve according to a vector autoregressive process that accounts for lagged and contemporaneous dependence across nodes and features, a characteristic neglected in the LSM literature. A Bayesian approach is used to address two of the primary sources of inference intractability in dynamic LSMs: latent feature estimation and the choice of latent space dimension. We employ an efficient auxiliary-mixture sampler that performs data augmentation and supports conditionally conjugate prior distributions. A point-process representation of the network weights and the finite-dimensional distribution of the latent processes are used to derive a multi-move sampler in which each feature trajectory is drawn in a single block, without recursions. This sampling strategy is new to the network literature and can significantly reduce computational time while improving chain mixing. To avoid trans-dimensional samplers, a Laplace approximation of the partial marginal likelihood is used to design a partially collapsed Gibbs sampler. Overall, our procedure is general, as it can be easily adapted to static and dynamic settings, as well as to other discrete or continuous weight distributions.

研究动机与目标

• Motivate and address the analysis of dynamic, weighted networks with counts and excess zeros.
• Propose a dynamic zero-inflated latent space eigenmodel where edge weights depend on latent feature similarity.
• Develop a scalable Bayesian inference scheme that jointly infers latent features, their dimension, and dynamic structure.
• Introduce computational innovations (auxiliary mixture sampler, AWOL sampling, Laplace-based dimension handling) to improve mixing and speed.
• Provide flexible model specifications (node-wise vs. feature-wise) to capture dependence and sparsity in temporal networks.

提出的方法

• Define y_{ij,t} as a zero-inflated Poisson with intensity \u0003bb_{ij,t} determined by latent features via log(\u0003bb_{ij,t}) = \u0000b5_i + \u0000b5_j + x_{i:,t}' \u001bXi x_{j:,t}.
• Model latent features X_t with a matrix autoregression X_t = ﾢe\u0000b1 X_{t-1} \u001a' + H_t, with H_t following a matrix normal distribution.
• Introduce an auxiliary allocation w_{ij,t} for zero inflation and a probit latent variable z_{ij,t} to handle zero-prone edges.
• Employ an improved auxiliary mixture sampler (IAMS) to convert Poisson likelihoods into conditionally Gaussian form for conjugate updates.
• Use a partially collapsed Gibbs sampler to infer the latent space dimension d and the latent trajectories without trans-dimensional moves.
• Provide two parsimonious parameterisations (node-wise vs. feature-wise) for the latent dynamics and discuss their implications.

实验结果

研究问题

• RQ1 如何将动态潜在空间模型扩展为具计数与过多零的加权网络？
• RQ2 是否可以在贝叶斯框架下同时推断动态网络的潜在节点特征与潜在空间维度？
• RQ3 特征导向的指定是否在捕捉同步节点依赖方面优于传统的节点导向方法？
• RQ4 如何通过辅助数据增广与部分坍缩采样在计数的动态LSM中提升计算效率与混合性？
• RQ5 零膨胀泊松动力学在现实世界的时序网络（如投票、贸易、脑连接）中的实际含义是什么？

主要发现

• 所提出的动态零膨胀潜在空间特征矩阵模型能够处理整数权重、过多零、节点位置随时间的变化以及稀疏性的变化。
• 辅助混合采样器使泊松部分在条件上变为高斯形式，从而实现共轭更新并提升MCMC效率。
• 基于AWOL的全序列样本采样器在不循环的情况下抽取完整潜在轨迹，改善混合性并降低计算量。
• 基于Laplace近似的部分坍缩吉布斯采样器避免跨维度移动，用以推断潜在维度d。
• 两种参数化（节点导向与特征导向）配合不同先验（逆Wishart vs. 图形阻尼刀伪）提供对依赖性与高维性的灵活处理。
• 采样器在推断潜在空间维度的同时联合推断潜在特征，量化不确定性而非依赖固定的d或信息准则。