# Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes

arXiv: https://arxiv.org/abs/2407.16935 · HTML: https://mlsanity.com/paper/2407.16935/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Federated Learning for Generalization, Robustness, Fairness: A Survey and Benchmark](https://mlsanity.com/paper/2311.06750/) (2023)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [FedPop: A Bayesian Approach for Personalised Federated Learning](https://mlsanity.com/paper/2206.03611/) (2022)
- [Spectral Mixture Kernels for Multi-Output Gaussian Processes](https://mlsanity.com/paper/1709.01298/) (2017)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (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)
- [Scalable Joint Models for Reliable Uncertainty-Aware Event Prediction](https://mlsanity.com/paper/1708.04757/) (2017)
- [The Gaussian Process Autoregressive Regression Model (GPAR)](https://mlsanity.com/paper/1802.07182/) (2018)
- [Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling](https://mlsanity.com/paper/2111.14008/) (2021)
- [Multi-Output Gaussian Processes for Crowdsourced Traffic Data Imputation](https://mlsanity.com/paper/1812.08739/) (2018)
- [Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach](https://mlsanity.com/paper/1901.11512/) (2019)
- [Generalized Multi-Output Gaussian Process Censored Regression](https://mlsanity.com/paper/2009.04822/) (2020)
- [On Negative Transfer and Structure of Latent Functions in Multi-output Gaussian Processes](https://mlsanity.com/paper/2004.02382/) (2020)
- [Multi-output Gaussian Process Modulated Poisson Processes for Event Prediction](https://mlsanity.com/paper/2011.03172/) (2020)
- [Federated Bayesian Neural Regression: A Scalable Global Federated Gaussian Process](https://mlsanity.com/paper/2206.06357/) (2022)
- [Grouped Gaussian Processes for Solar Power Prediction](https://mlsanity.com/paper/1806.02543/) (2018)
- [Weakly-supervised Multi-output Regression via Correlated Gaussian Processes](https://mlsanity.com/paper/2002.08412/) (2020)

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

- [Gait-Based Hand Load Estimation via Deep Latent Variable Models with Auxiliary Information](https://mlsanity.com/paper/2507.05544/) (2025)
- [Scalable Asynchronous Federated Modeling for Spatial Data](https://mlsanity.com/paper/2510.01771/) (2025)
- [Personalized Federated Hierarchical Gaussian Processes for Privacy-Preserving Modeling of Heterogeneous Distributed Systems](https://mlsanity.com/paper/2609.19337/) (2026)

## Abstract (arXiv)

This paper explores a federated learning approach that automatically selects the number of latent processes in multi-output Gaussian processes (MGPs). The MGP has seen great success as a transfer learning tool when data is generated from multiple sources/units/entities. A common approach in MGPs to transfer knowledge across units involves gathering all data from each unit to a central server and extracting common independent latent processes to express each unit as a linear combination of the shared latent patterns. However, this approach poses key challenges in (i) determining the adequate number of latent processes and (ii) relying on centralized learning which leads to potential privacy risks and significant computational burdens on the central server. To address these issues, we propose a hierarchical model that places spike-and-slab priors on the coefficients of each latent process. These priors help automatically select only needed latent processes by shrinking the coefficients of unnecessary ones to zero. To estimate the model while avoiding the drawbacks of centralized learning, we propose a variational inference-based approach, that formulates model inference as an optimization problem compatible with federated settings. We then design a federated learning algorithm that allows units to jointly select and infer the common latent processes without sharing their data. We also discuss an efficient learning approach for a new unit within our proposed federated framework. Simulation and case studies on Li-ion battery degradation and air temperature data demonstrate the advantageous features of our proposed approach.