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：本文针对加权时序网络提出了一种新的动态潜在空间本征模型（LSM）。该模型可容纳整数值权重、零膨胀现象、时变节点位置（特征）以及时变网络稀疏性。潜在位置根据向量自回归过程演化，该过程考虑了节点与特征之间的滞后依赖和同期依赖，这是LSM文献中常被忽视的特性。采用贝叶斯方法解决动态LSM中两个主要的推断困难：潜在特征估计和潜在空间维度的选择。我们使用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。通过网络权重点过程表示与潜在过程的有限维分布，推导出一种多移动采样器，其中每个特征轨迹以单一数据块形式完整抽取，无需递归递推。这种采样策略在网络文献中具有创新性，能够显著减少计算时间并改善链的混合效率。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，可便捷适配于静态与动态场景，以及其他离散或连续权重分布。