Background: In biomedical applications, valuable data is often split between owners who cannot openly share the data because of privacy regulations and concerns. Training Machine Learning models on the joint data without violating privacy is a major technology challenge that can be addressed by combining techniques from Machine Learning and cryptography. When collaboratively training Machine Learning models with the cryptographic technique named secure Multi-Party Computation, the price paid for keeping the data of the owners private is an increase in computational cost and runtime. A careful choice of Machine Learning techniques, algorithmic and implementation optimizations are a necessity to enable practical secure Machine Learning over distributed data sets. Such optimizations can be tailored to the kind of data and Machine Learning problem at hand.
Methods: Our setup involves secure Two-Party Computation protocols, along with a trusted initializer that distributes correlated randomness to the two computing parties. We use a gradient descent based algorithm for training a logistic regression model, and we break down the algorithm into corresponding cryptographic protocols. Our main contributions are a new protocol for computing the activation function that requires neither secure comparison protocols nor Yao's garbled circuits, and a series of cryptographic engineering optimizations to improve the performance.
Results: For our largest gene expression data set, we train a model that requires over 7 billion secure multiplications; the training completes in about 26.90 seconds in a local area network. The implementation in this work is a further optimized version of the implementation with which we won first place in Track 4 of the iDASH 2019 secure genome analysis competition.
Conclusions: In this paper, we present a secure logistic regression training protocol and its implementation, with a new subprotocol to securely compute the activation function. To the best of our knowledge, we present the fastest existing secure Multi-Party Computation implementation for training logistic regression models on high dimensional genome data distributed across a local area network.