Federated Gaussian Process Regression with Orthogonal Feature Encryption and Key-Based Access Control

Federated learning (FL) makes it possible to train models across distributed data sources without collecting raw data in one place. However, even in federated settings, trained models may still leak sensitive information at inference time. This problem is particularly evident for Gaussian Process regression (GPR), where predictive uncertainty is explicitly returned and can differ between training and non-training samples. Such differences can be exploited for membership inference. In this work, we examine inference-time privacy and robustness in federated GPR by focusing on the behavior of predictive variance. To enable scalable training, we employ a Random Fourier Feature approximation together with an Alternating Direction Method of Multipliers (ADMM) based distributed optimization scheme. On top of this learning framework, we apply key-dependent orthogonal feature transformations that enable multi-key inference time access control. When inference is performed using the correct key, prediction accuracy and uncertainty behavior remain close to those of plaintext federated GPR. When incorrect or mismatched keys are used, prediction errors increase sharply and predictive variance becomes uniformly large. Experimental results show that this variance inflation removes the usual gap between training and unseen samples, reducing the effectiveness of variance-based membership inference. Importantly, this effect arises without adding noise or relying on cryptographic operations. These findings suggest that predictive uncertainty can play a practical role in enforcing inference-time access control and improving privacy robustness in federated Gaussian Process models.

@article{Islam2026,
  title     = {Federated Gaussian Process Regression with Orthogonal Feature Encryption and Key-Based Access Control},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {17},
  number    = {3},
  year      = {2026},
  publisher = {The Science and Information Organization},
  author    = {Md. Rashedul Islam and Jannatul Ferdous Akhi and Takayuki Nakachi},
  doi       = {10.14569/IJACSA.2026.0170305},
  url       = {https://doi.org/10.14569/IJACSA.2026.0170305}
}