B1018
Title: Factorized fusion shrinkage for dynamic relational data
Authors: Peng Zhao - University of Delaware (United States) [presenting]
Anirban Bhattacharya - Texas AM University (United States)
Debdeep Pati - Texas A&M University (United States)
Bani Mallick - Texas A&M University (United States)
Abstract: Modern data science applications often involve complex relational data with dynamic structures. In systems that experience regime changes, such as changes in alliances between nations after a war or air transportation networks in the wake of the COVID-19 pandemic, abrupt alterations in the relational dynamics of such data are commonly observed. To address this, a factorized fusion shrinkage model is proposed, which consists of a dynamic shrinkage of each decomposed factor towards a group-wise fusion structure, where shrinkage is achieved through the application of global-local shrinkage priors to successive differences in the row vectors of the factorized matrices. The priors employed in the model preserve both the separability of clusters and the long-range properties of latent factor dynamics. Under specific conditions, it is proven that the posterior distribution of the model attains the minimax optimal rate up to logarithmic factors. In terms of computation, a structured mean-field variational inference algorithm is introduced that balances optimal posterior inference with computational scalability. The framework leverages both the inter-component dependence and the temporal dependence across time. The framework is versatile and can accommodate a wide range of models, including latent space models for networks, dynamic matrix factorization, and low-rank tensor models. The efficacy of the methodology is tested through extensive simulations and real-world data analysis.
