DMS Statistics and Data Science Seminar

Speaker: Marco Avella Medina (Columbia University)

Title: Differentially private high-dimensional M-estimation via noisy optimization

Abstract: We consider a general optimization-based framework for computing differentially private high-dimensional M-estimators and a new method for constructing differentially private confidence regions. In particular, we show how to construct differentially private penalized M-estimators via a noisy projected gradient descent algorithm that obtains global linear convergence under local restricted strong convexity. Our analysis shows that our estimators converge with high probability to a nearly optimal neighborhood of the non-private M-estimators. We then tackle the problem of parametric inference by constructing a differentially private version of a debiased lasso procedure. This enables us to construct confidence regions and to conduct hypothesis testing, based on private approximate pivots. We illustrate the performance of our methods in several numerical examples.

This is joint work with Po-Ling Loh and Zheng Liu.