# Bayesian Spillover Graphs for Dynamic Networks

arXiv: https://arxiv.org/abs/2203.01912 · HTML: https://mlsanity.com/paper/2203.01912/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 40 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Dynamic Shrinkage Processes](https://mlsanity.com/paper/1707.00763/) (2017)

## Built on by (most cited first, 1 of 1)

- [Learning Time-Varying Graphs from Incomplete Graph Signals](https://mlsanity.com/paper/2510.17903/) (2025)

## Abstract (arXiv)

We present Bayesian Spillover Graphs (BSG), a novel method for learning temporal relationships, identifying critical nodes, and quantifying uncertainty for multi-horizon spillover effects in a dynamic system. BSG leverages both an interpretable framework via forecast error variance decompositions (FEVD) and comprehensive uncertainty quantification via Bayesian time series models to contextualize temporal relationships in terms of systemic risk and prediction variability. Forecast horizon hyperparameter h allows for learning both short-term and equilibrium state network behaviors. Experiments for identifying source and sink nodes under various graph and error specifications show significant performance gains against state-of-the-art Bayesian Networks and deep-learning baselines. Applications to real-world systems also showcase BSG as an exploratory analysis tool for uncovering indirect spillovers and quantifying systemic risk.