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.

翻译：针对加权时序网络，本文提出一种新的动态潜在空间特征模型（LSM）。该模型能够处理整数值权重、零膨胀现象、时变节点位置（特征）以及时变网络稀疏性。潜在位置遵循向量自回归过程演化，刻画了跨节点与特征的滞后与同期依赖性——这一特性在现有LSM文献中常被忽略。采用贝叶斯方法解决动态LSM中两个核心推断难题：潜在特征估计与潜在空间维度选择。我们设计了一种高效的辅助混合采样器，通过数据增广支持条件共轭先验分布。利用网络权重点过程表征与潜在过程的有限维分布，推导出多步采样器，使得每条特征轨迹能够在单个区块中实现无递归抽取。这种采样策略在网络文献中尚属首次，可在提升链混合效率的同时显著降低计算时间。为避免跨维度采样器，采用部分边际似然的拉普拉斯近似设计部分折叠吉布斯采样器。总体而言，本方法具有通用性，可便捷适配静态与动态场景，以及其它离散或连续权重分布。