Modern data science applications often involve complex relational data with dynamic structures. An abrupt change in such dynamic relational data is typically observed in systems that undergo regime changes due to interventions. In such a case, we consider a factorized fusion shrinkage model in which all decomposed factors are dynamically shrunk towards group-wise fusion structures, where the shrinkage is obtained by applying global-local shrinkage priors to the successive differences of the row vectors of the factorized matrices. The proposed priors enjoy many favorable properties in comparison and clustering of the estimated dynamic latent factors. Comparing estimated latent factors involves both adjacent and long-term comparisons, with the time range of comparison considered as a variable. Under certain conditions, we demonstrate that the posterior distribution attains the minimax optimal rate up to logarithmic factors. In terms of computation, we present a structured mean-field variational inference framework that balances optimal posterior inference with computational scalability, exploiting both the dependence among components and across time. The framework can accommodate a wide variety of models, including dynamic matrix factorization, latent space models for networks and low-rank tensors. The effectiveness of our methodology is demonstrated through extensive simulations and real-world data analysis.

翻译：现代数据科学应用常涉及具有动态结构的复杂关系数据。此类动态关系数据中的突变通常出现在因干预而发生体制变化的系统中。针对这种情况，我们提出一种因子化融合收缩模型，其中所有分解因子均动态收缩至组间融合结构，该收缩通过将全局-局部收缩先验应用于因子化矩阵行向量的连续差分而实现。所提先验在估计动态潜在因子的比较与聚类方面具有诸多优良特性。潜在因子的比较包含相邻比较与长期比较，其中比较的时间范围被视为变量。在特定条件下，我们证明后验分布能以对数因子达到极小极大最优速率。在计算方面，我们提出一种结构化平均场变分推断框架，该框架通过同时利用分量间依赖性与时间维度依赖性，在最优后验推断与计算可扩展性之间取得平衡。该框架可适用于多种模型，包括动态矩阵分解、网络潜在空间模型及低秩张量模型。通过大量仿真实验与真实数据分析，验证了所提方法的有效性。