Differentially Private Conformal Prediction via Quantile Binary Search

Abstract

Differentially Private (DP) approaches have been widely explored and implemented for a broad variety of tasks delivering corresponding privacy guarantees in these settings. While most of these DP approaches focus on limiting privacy leakage from training data, there are fewer approaches that consider leakage when procedures involve \textit{calibration data} which is common in uncertainty quantification through Conformal Prediction (CP). Since there is a limited amount of approaches in this direction, in this work we deliver a general DP approach for CP that we call Private Conformity via Quantile Search (P-COQS). The proposed approach adapts an existing randomized binary search algorithm for computing DP quantiles in the calibration phase of CP thereby guaranteeing privacy of the consequent prediction sets. This however comes at a price of marginally under-covering with respect to the desired $(1 - \alpha)$-level when using finite-sample calibration sets (although broad empirical results show that the P-COQS generally targets the required level in the considered cases). Confirming properties of the adapted algorithm and quantifying the approximate coverage guarantees of the consequent CP, we conduct extensive experiments to examine the effects of privacy noise, sample size and significance level on the performance of P-COQS compared to existing alternatives. In addition, we empirically evaluate our approach on several benchmark datasets, including CIFAR-10, ImageNet and CoronaHack. Our results suggest that the proposed method is robust to privacy noise and performs favorably with respect to the current DP alternative in terms of \textit{empirical coverage}, \textit{efficiency}, and \textit{informativeness}. Specifically, the results indicate that P-COQS produces smaller conformal prediction sets while simultaneously targeting the desired coverage and privacy guarantees in all these experimental settings.