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How to properly set the privacy parameter in differential privacy (DP) hasbeen an open question in DP research since it was first proposed in 2006. Inthis work, we demonstrate the ability of influence functions to offer insightinto how a specific privacy parameter value will affect a model's test loss inthe randomized response-based local DP setting. Our proposed method allows adata curator to select the privacy parameter best aligned with their allowedprivacy-utility trade-off without requiring heavy computation such as extensivemodel retraining and data privatization. We consider multiple commonrandomization scenarios, such as performing randomized response over thefeatures, and/or over the labels, as well as the more complex case of applyinga class-dependent label noise correction method to offset the noise incurred byrandomization. Further, we provide a detailed discussion over the computationalcomplexity of our proposed approach inclusive of an empirical analysis. Throughempirical evaluations we show that for both binary and multi-class settings,influence functions are able to approximate the true change in test loss thatoccurs when randomized response is applied over features and/or labels withsmall mean absolute error, especially in cases where noise correction methodsare applied.

Evaluating the Impact of Local Differential Privacy on Utility Loss via Influence Functions