Dynamic latent space models are widely used for characterizing changes in networks and relational data over time. These models assign to each node latent attributes that characterize connectivity with other nodes, with these latent attributes dynamically changing over time. Node attributes can be organized as a three-way tensor with modes corresponding to nodes, latent space dimension, and time. Unfortunately, as the number of nodes and time points increases, the number of elements of this tensor becomes enormous, leading to computational and statistical challenges, particularly when data are sparse. We propose a new approach for massively reducing dimensionality by expressing the latent node attribute tensor as low rank. This leads to an interesting new nested exemplar latent space model, which characterizes the node attribute tensor as dependent on low-dimensional exemplar traits for each node, weights for each latent space dimension, and exemplar curves characterizing time variation. We study properties of this framework, including expressivity, and develop efficient Bayesian inference algorithms. The approach leads to substantial advantages in simulations and applications to ecological networks.

翻译：动态潜空间模型被广泛用于刻画网络和关系数据随时间的变化。这些模型为每个节点分配潜属性，以表征其与其他节点的连接性，这些潜属性随时间动态变化。节点属性可组织为三阶张量，其模态分别对应节点、潜空间维度和时间。然而，随着节点数量和时间点的增加，该张量的元素数量变得极其庞大，导致计算和统计上的挑战，尤其在数据稀疏时更为突出。我们提出一种通过将节点潜属性张量表达为低秩形式来大幅降低维度的新方法。这导出了一个新颖的嵌套范例潜空间模型，该模型将节点属性张量表征为依赖于每个节点的低维范例特征、每个潜空间维度的权重以及刻画时间变化的范例曲线。我们研究了该框架的性质，包括表达能力，并开发了高效的贝叶斯推断算法。该方法在模拟和生态网络应用中展现出显著优势。