Resampling methods for private statistical inference
This work addresses the need for private statistical inference, offering improved efficiency for applications requiring data privacy, though it is incremental as it builds on existing bootstrap methods.
The paper tackles the problem of constructing confidence intervals with differential privacy by proposing two private variants of the non-parametric bootstrap, achieving error rates comparable to non-private methods within logarithmic factors and providing notably shorter confidence intervals (≥10 times) than previous approaches.
We consider the task of constructing confidence intervals with differential privacy. We propose two private variants of the non-parametric bootstrap, which privately compute the median of the results of multiple "little" bootstraps run on partitions of the data and give asymptotic bounds on the coverage error of the resulting confidence intervals. For a fixed differential privacy parameter $ε$, our methods enjoy the same error rates as that of the non-private bootstrap to within logarithmic factors in the sample size $n$. We empirically validate the performance of our methods for mean estimation, median estimation, and logistic regression with both real and synthetic data. Our methods achieve similar coverage accuracy to existing methods (and non-private baselines) while providing notably shorter ($\gtrsim 10$ times) confidence intervals than previous approaches.