Secure Linear Regression on Vertically Partitioned Datasets

We propose multi-party computation protocols for securely computing a linear regression model from a training dataset whose columns are distributed among several parties. Our solution enables organizations to collaborate in the construction of a predictive model while keeping their training data private. Our approach is based on a hybrid MPC protocol combining garbled circuits with an offline phase enabled by a semi-trusted external party. As part of our contribution, we evaluate several algorithms and implementations for solving systems of linear equations using garbled circuts. Experiments conducted with an implementation of our protocols show that our approach leads to highly scalable solutions that can solve data analysis problems with one million records and one hundred features in less than one hour.