Privacy-preserving kriging interpolation on partitioned data

Abstract

Kriging is well-known, frequently applied method in geo-statistics. Its success primarily depends on the total number of measurements for some sample points. If there are sufficient sample points with measurements, kriging will reflect the surface accurately. Obtaining a sufficient number of measurements can be costly and time-consuming. Thus, different companies might obtain a limited number of measurements of the same region and want to offer predictions collaboratively. However, due to privacy concerns, they might hesitate to cooperate with each other. In this paper, we propose a protocol to estimate kriging-based predictions using partitioned data from two parties while preserving their confidentiality. Our protocol also protects a client's privacy. The proposed method helps two servers create models based on split data without divulging private data and provide predictions to their clients while preserving the client's confidentiality. We analyze the scheme with respect to privacy, performance, and accuracy. Our theoretical analysis shows that it achieves privacy. Although it causes some additional costs, they are not critical to overall performance. Our real data-based empirical outcomes show that our method is able to offer accurate predictions even if there are accuracy losses due to privacy measures