Factorized Fusion Shrinkage for Dynamic Relational Data

TL;DR

This paper introduces a factorized fusion shrinkage model for dynamic relational data, enabling effective clustering and change detection in systems with regime shifts, with theoretical guarantees and scalable inference methods.

Contribution

It proposes a novel shrinkage prior-based model for dynamic latent factors, with a scalable variational inference framework applicable to various complex data structures.

Findings

Achieves near-minimax optimal posterior contraction rates.

Demonstrates effective clustering of dynamic latent factors.

Shows superior performance in simulations and real data applications.

Abstract

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.