Practical Privacy-Preserving Gaussian Process Regression via Secret Sharing

Gaussian process regression (GPR) is a non-parametric model that has been used in many real-world applications that involve sensitive personal data (e.g., healthcare, finance, etc.) from multiple data owners. To fully and securely exploit the value of different data sources, this paper proposes a privacy-preserving GPR method based on secret sharing (SS), a secure multi-party computation (SMPC) technique. In contrast to existing studies that protect the data privacy of GPR via homomorphic encryption, differential privacy, or federated learning, our proposed method is more practical and can be used to preserve the data privacy of both the model inputs and outputs for various data-sharing scenarios (e.g., horizontally/vertically-partitioned data). However, it is non-trivial to directly apply SS on the conventional GPR algorithm, as it includes some operations whose accuracy and/or efficiency have not been well-enhanced in the current SMPC protocol. To address this issue, we derive a new SS-based exponentiation operation through the idea of "confusion-correction" and construct an SS-based matrix inversion algorithm based on Cholesky decomposition. More importantly, we theoretically analyze the communication cost and the security of the proposed SS-based operations. Empirical results show that our proposed method can achieve reasonable accuracy and efficiency under the premise of preserving data privacy.