Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain
This work addresses the problem of improving differentially private linear regression for statisticians and machine learning practitioners, though it is incremental as it builds on existing algorithms.
The authors revisited differentially private linear regression, clarifying how feature, label, and coefficient domains affect optimization and estimation errors, and proposed adaptive modifications to two existing algorithms (posterior sampling and sufficient statistics perturbation) that exploit data-dependent quantities. Experiments on 36 datasets showed both AdaOPS and AdaSSP outperformed existing techniques on nearly all datasets.
We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization error and estimation error, hence revealing the delicate price of differential privacy in statistical estimation and statistical learning. Moreover, we propose simple modifications of two existing DP algorithms: (a) posterior sampling, (b) sufficient statistics perturbation, and show that they can be upgraded into **adaptive** algorithms that are able to exploit data-dependent quantities and behave nearly optimally **for every instance**. Extensive experiments are conducted on both simulated data and real data, which conclude that both AdaOPS and AdaSSP outperform the existing techniques on nearly all 36 data sets that we test on.