Privacy-aware Gaussian Process Regression

2023-05-25

arXiv.org

AI Summary

Data owners often refuse to release high-fidelity Gaussian process regression (GPR) models due to privacy concerns. Method: This paper proposes a differential-privacy-inspired noise injection framework that synthesizes a controllable covariance matrix for additive noise, ensuring the predictive variance strictly satisfies a pre-specified privacy threshold. Contribution/Results: We establish, for the first time, a theoretical modeling and optimization framework for GPR under privacy constraints; develop an optimal noise covariance computation algorithm based on semidefinite programming (SDP); and generalize the formulation to a unified kernel-method representation under continuous privacy constraints. Empirical evaluation on satellite trajectory tracking demonstrates tunable accuracy–privacy trade-offs. Theoretical analysis guarantees both strict adherence to the prescribed privacy budget and an upper bound on generalization error.

Abstract

We propose the first theoretical and methodological framework for Gaussian process regression subject to privacy constraints. The proposed method can be used when a data owner is unwilling to share a high-fidelity supervised learning model built from their data with the public due to privacy concerns. The key idea of the proposed method is to add synthetic noise to the data until the predictive variance of the Gaussian process model reaches a prespecified privacy level. The optimal covariance matrix of the synthetic noise is formulated in terms of semi-definite programming. We also introduce the formulation of privacy-aware solutions under continuous privacy constraints using kernel-based approaches, and study their theoretical properties. The proposed method is illustrated by considering a model that tracks the trajectories of satellites.

Problem

• Develops privacy-preserving Gaussian process regression with synthetic noise
• Addresses data owners' unwillingness to share sensitive supervised models
• Formulates optimal noise covariance via semi-definite programming

Innovation

• Adding synthetic noise to Gaussian process data
• Optimizing noise covariance via semi-definite programming
• Implementing continuous privacy constraints with kernels