  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.
