Differentially private inference via noisy optimization

Understand

We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions.

• Firstly, we show that robust statistics can be used in conjunction with noisy gradient descent or noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively.
• We establish local and global convergence guarantees, under both local strong convexity and self-concordance, showing that our private estimators converge with high probability to a small neighborhood of the non-private M-estimators.
• Secondly, we tackle the problem of parametric inference by constructing differentially private estimators of the asymptotic variance of our private M-estimators.