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In recent years, formal methods of privacy protection such as differentialprivacy (DP), capable of deployment to data-driven tasks such as machinelearning (ML), have emerged. Reconciling large-scale ML with the closed-formreasoning required for the principled analysis of individual privacy lossrequires the introduction of new tools for automatic sensitivity analysis andfor tracking an individual's data and their features through the flow ofcomputation. For this purpose, we introduce a novel \textit{hybrid} automaticdifferentiation (AD) system which combines the efficiency of reverse-mode ADwith an ability to obtain a closed-form expression for any given quantity inthe computational graph. This enables modelling the sensitivity of arbitrarydifferentiable function compositions, such as the training of neural networkson private data. We demonstrate our approach by analysing the individual DPguarantees of statistical database queries. Moreover, we investigate theapplication of our technique to the training of DP neural networks. Ourapproach can enable the principled reasoning about privacy loss in the settingof data processing, and further the development of automatic sensitivityanalysis and privacy budgeting systems.

Sensitivity analysis in differentially private machine learning using hybrid automatic differentiation