# Personalized Federated Hierarchical Gaussian Processes for Privacy-Preserving Modeling of Heterogeneous Distributed Systems

arXiv: https://arxiv.org/abs/2609.19337 · HTML: https://mlsanity.com/paper/2609.19337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1806.00720/) (2018)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)
- [The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning](https://mlsanity.com/paper/2111.05326/) (2021)
- [The role of surrogate models in the development of digital twins of dynamic systems](https://mlsanity.com/paper/2001.09292/) (2020)
- [Distributed Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models](https://mlsanity.com/paper/1402.1389/) (2014)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process Regression](https://mlsanity.com/paper/1412.3078/) (2014)
- [Federated Data Analytics: A Study on Linear Models](https://mlsanity.com/paper/2206.07786/) (2022)
- [Asynchronous Distributed Variational Gaussian Processes for Regression](https://mlsanity.com/paper/1704.06735/) (2017)
- [Federated Bayesian Neural Regression: A Scalable Global Federated Gaussian Process](https://mlsanity.com/paper/2206.06357/) (2022)
- [Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning](https://mlsanity.com/paper/2203.02865/) (2022)
- [Federated Learning for Predictive Maintenance and Quality Inspection in Industrial Applications](https://mlsanity.com/paper/2304.11101/) (2023)
- [Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes](https://mlsanity.com/paper/2407.16935/) (2024)
- [Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data](https://mlsanity.com/paper/2309.03439/) (2023)
- [Robust, Online, and Adaptive Decentralized Gaussian Processes](https://mlsanity.com/paper/2509.18011/) (2025)

## Abstract (arXiv)

We present Personalized Federated Hierarchical Gaussian Processes (pFedHGP) for probabilistic regression and classification when data are distributed across heterogeneous clients. Each client's latent function decomposes into (i) a shared global component, (ii) a client-specific deviation that shares the global kernel structure, and (iii) a flexible local residual. Sparse inducing-variable approximations and federated variational inference keep raw data local while the server synchronizes only low-dimensional statistics for the shared component. Full predictive distributions support uncertainty-aware decisions. In application studies, pFedHGP attains perfect fault classification in press tonnage monitoring using 13.77% of labeled cycles and recovers geographic zones in federated air-quality modeling without centralizing station-level time series. An Instantaneous Linear Mixing Model viewpoint links the hierarchy to multi-output Gaussian processes for correlated sensors.