# Factorized Fusion Shrinkage for Dynamic Relational Data

arXiv: https://arxiv.org/abs/2210.00091 · HTML: https://mlsanity.com/paper/2210.00091/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 86 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [The structure and dynamics of multilayer networks](https://mlsanity.com/paper/1407.0742/) (2014)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Scalable Link Prediction in Dynamic Networks via Non-Negative Matrix Factorization](https://mlsanity.com/paper/1411.3675/) (2014)
- [Factor Models for High-Dimensional Tensor Time Series](https://mlsanity.com/paper/1905.07530/) (2019)
- [ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise](https://mlsanity.com/paper/2009.12297/) (2020)
- [Spectral clustering in the dynamic stochastic block model](https://mlsanity.com/paper/1705.01204/) (2017)
- [Dynamic Tensor Recommender Systems](https://mlsanity.com/paper/2003.05568/) (2020)
- [Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning](https://mlsanity.com/paper/1810.09569/) (2018)
- [Nonparametric Bayes dynamic modeling of relational data](https://mlsanity.com/paper/1311.4669/) (2013)
- [Decoupling shrinkage and selection in Bayesian linear models: a posterior summary perspective](https://mlsanity.com/paper/1408.0464/) (2014)
- [Dynamic Shrinkage Processes](https://mlsanity.com/paper/1707.00763/) (2017)
- [A Variational Algorithm for Bayesian Variable Selection](https://mlsanity.com/paper/1602.07640/) (2016)
- [Bayesian sparse multiple regression for simultaneous rank reduction and variable selection](https://mlsanity.com/paper/1612.00877/) (2016)
- [Recovery of simultaneous low rank and two-way sparse coefficient matrices, a nonconvex approach](https://mlsanity.com/paper/1802.06967/) (2018)
- [On the identifiability of Bayesian factor analytic models](https://mlsanity.com/paper/2004.05105/) (2020)
- [Latent Space Approaches to Community Detection in Dynamic Networks](https://mlsanity.com/paper/2005.08276/) (2020)
- [An Eigenmodel for Dynamic Multilayer Networks](https://mlsanity.com/paper/2103.12831/) (2021)
- [Local Gaussian Process Model for Large-scale Dynamic Computer Experiments](https://mlsanity.com/paper/1611.09488/) (2016)
- [Structured Optimal Variational Inference for Dynamic Latent Space Models](https://mlsanity.com/paper/2209.15117/) (2022)
- [Detecting Structural Changes in Longitudinal Network Data](https://mlsanity.com/paper/1811.01384/) (2018)
- [Post-Processed Posteriors for Sparse Covariances and Its Application to Global Minimum Variance Portfolio](https://mlsanity.com/paper/2108.09462/) (2021)

## Abstract (arXiv)

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.