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Differential privacy allows bounding the influence that training data recordshave on a machine learning model. To use differential privacy in machinelearning, data scientists must choose privacy parameters $(\epsilon,\delta)$.Choosing meaningful privacy parameters is key, since models trained with weakprivacy parameters might result in excessive privacy leakage, while strongprivacy parameters might overly degrade model utility. However, privacyparameter values are difficult to choose for two main reasons. First, thetheoretical upper bound on privacy loss $(\epsilon,\delta)$ might be loose,depending on the chosen sensitivity and data distribution of practicaldatasets. Second, legal requirements and societal norms for anonymization oftenrefer to individual identifiability, to which $(\epsilon,\delta)$ are onlyindirectly related.  We transform $(\epsilon,\delta)$ to a bound on the Bayesian posterior beliefof the adversary assumed by differential privacy concerning the presence of anyrecord in the training dataset. The bound holds for multidimensional queriesunder composition, and we show that it can be tight in practice. Furthermore,we derive an identifiability bound, which relates the adversary assumed indifferential privacy to previous work on membership inference adversaries. Weformulate an implementation of this differential privacy adversary that allowsdata scientists to audit model training and compute empirical identifiabilityscores and empirical $(\epsilon,\delta)$.

Quantifying identifiability to choose and audit $\epsilon$ in differentially private deep learning