# Federated Granger Causality Learning for Interdependent Clients with State Space Representation

arXiv: https://arxiv.org/abs/2501.13890 · HTML: https://mlsanity.com/paper/2501.13890/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 23 Jan 2025.

## Builds on (most cited first, 19 of 19)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [SplitFed: When Federated Learning Meets Split Learning](https://mlsanity.com/paper/2004.12088/) (2020)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Private federated learning on vertically partitioned data via entity resolution and additively homomorphic encryption](https://mlsanity.com/paper/1711.10677/) (2017)
- [Privacy Preserving Vertical Federated Learning for Tree-based Models](https://mlsanity.com/paper/2008.06170/) (2020)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [Split Learning for collaborative deep learning in healthcare](https://mlsanity.com/paper/1912.12115/) (2019)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [A Quasi-Newton Method Based Vertical Federated Learning Framework for Logistic Regression](https://mlsanity.com/paper/1912.00513/) (2019)
- [Large-Scale Secure XGB for Vertical Federated Learning](https://mlsanity.com/paper/2005.08479/) (2020)
- [Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components](https://mlsanity.com/paper/1411.3972/) (2014)
- [Federated Learning of Models Pre-Trained on Different Features with Consensus Graphs](https://mlsanity.com/paper/2306.01240/) (2023)
- [Subspace identification of large-scale interconnected systems](https://mlsanity.com/paper/1309.5105/) (2013)
- [Decentralized Control via Dynamic Stochastic Prices: The Independent System Operator Problem](https://mlsanity.com/paper/1605.08926/) (2016)
- [Partition-based Distributed Kalman Filter with plug and play features](https://mlsanity.com/paper/1507.06820/) (2015)

## Built on by (most cited first, 3 of 3)

- [Federated Causal Representation Learning in State-Space Systems for Decentralized Counterfactual Reasoning](https://mlsanity.com/paper/2602.19414/) (2026)
- [Uncertainty Quantification in Federated Granger Causality Learning](https://mlsanity.com/paper/2602.13004/) (2026)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## Abstract (arXiv)

Advanced sensors and IoT devices have improved the monitoring and control of complex industrial enterprises. They have also created an interdependent fabric of geographically distributed process operations (clients) across these enterprises. Granger causality is an effective approach to detect and quantify interdependencies by examining how one client's state affects others over time. Understanding these interdependencies captures how localized events, such as faults and disruptions, can propagate throughout the system, possibly causing widespread operational impacts. However, the large volume and complexity of industrial data pose challenges in modeling these interdependencies. This paper develops a federated approach to learning Granger causality. We utilize a linear state space system framework that leverages low-dimensional state estimates to analyze interdependencies. This addresses bandwidth limitations and the computational burden commonly associated with centralized data processing. We propose augmenting the client models with the Granger causality information learned by the server through a Machine Learning (ML) function. We examine the co-dependence between the augmented client and server models and reformulate the framework as a standalone ML algorithm providing conditions for its sublinear and linear convergence rates. We also study the convergence of the framework to a centralized oracle model. Moreover, we include a differential privacy analysis to ensure data security while preserving causal insights. Using synthetic data, we conduct comprehensive experiments to demonstrate the robustness of our approach to perturbations in causality, the scalability to the size of communication, number of clients, and the dimensions of raw data. We also evaluate the performance on two real-world industrial control system datasets by reporting the volume of data saved by decentralization.