Using Robust Estimation Theory to Design Efficient Secure Multiparty Linear Regression.

Various biomedical research studies, such as large-population studies and studies on rare diseases, require sharing of data across multiple sources or institutions. In fact, data sharing will enable the collection of more cases for analysis and thus increase the statistical power of the study. However, combining data from various sources poses privacy risks. A number of protocols have been proposed in the literature to address the privacy concerns; but these protocols do not fully deliver either on privacy or complexity. The main reason lies in the methodology used to design these secure algorithms. It is based on translating regular algorithms into secure versions using cryptographic procedures and tricks rather than on establishing robust theory for designing secure and communication free distributed algorithms. In this paper, we use well-established theoretical results to design a secure and low communication linear regression protocol. The method used is comprehensive and can be generalized to other estimators.