Roberto Molinari

Ogonnaya M. Romanus, Roberto Molinari

Most Differentially Private (DP) approaches focus on limiting privacy leakage from learners based on the data that they are trained on, there are fewer approaches that consider leakage when procedures involve a calibration dataset which is common in uncertainty quantification methods such as 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 slightly under-covering with respect to the desired $(1 - α)$-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 our approach 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 empirical coverage, efficiency, and 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.

Aleksandra Slavkovic, Roberto Molinari

Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP procedure should be similar in terms of their probability distribution. While DP mechanisms are provably effective in protecting privacy, they often negatively impact the utility of the query responses, statistics and/or analyses that come as outputs from these mechanisms. To address this problem, we use ideas from the area of robust statistics which aims at reducing the influence of outlying observations on statistical inference. Based on the preliminary known links between differential privacy and robust statistics, we modify the objective perturbation mechanism by making use of a new bounded function and define a bounded M-Estimator with adequate statistical properties. The resulting privacy mechanism, named "Perturbed M-Estimation", shows important potential in terms of improved statistical utility of its outputs as suggested by some preliminary results. These results consequently support the need to further investigate the use of robust statistical tools for differential privacy.

Roberto Molinari, Gaetan Bakalli, Stéphane Guerrier et al.

The majority of machine learning methods and algorithms give high priority to prediction performance which may not always correspond to the priority of the users. In many cases, practitioners and researchers in different fields, going from engineering to genetics, require interpretability and replicability of the results especially in settings where, for example, not all attributes may be available to them. As a consequence, there is the need to make the outputs of machine learning algorithms more interpretable and to deliver a library of "equivalent" learners (in terms of prediction performance) that users can select based on attribute availability in order to test and/or make use of these learners for predictive/diagnostic purposes. To address these needs, we propose to study a procedure that combines screening and wrapper approaches which, based on a user-specified learning method, greedily explores the attribute space to find a library of sparse learners with consequent low data collection and storage costs. This new method (i) delivers a low-dimensional network of attributes that can be easily interpreted and (ii) increases the potential replicability of results based on the diversity of attribute combinations defining strong learners with equivalent predictive power. We call this algorithm "Sparse Wrapper AlGorithm" (SWAG).