Preserving differential privacy has been well studied under centralized setting. However, its very challenging to preserve differential privacy under multiparty setting, especially for the vertically partitioned case. In this work, we propose a new framework for differential privacy preserving multiparty learning in the vertically partitioned setting. Our core idea is based on the functional mechanism that achieves differential privacy of the released model by adding noise to the objective function. We show the server can simply dissect the objective function into single-party and cross-party sub-functions, and allocate computation and perturbation of their polynomial coefficients to local parties. Our method needs only one round of noise addition and secure aggregation. The released model in our framework achieves the same utility as applying the functional mechanism in the centralized setting. Evaluation on real-world and synthetic datasets for linear and logistic regressions shows the effectiveness of our proposed method.
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