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Home | Events Archive | Differentially Private Inference via Noisy Optimization
Seminar

Differentially Private Inference via Noisy Optimization


  • Series
    Erasmus Econometric Institute Series
  • Speakers
    Marco Avella Medina (Columbia University, United States)
  • Field
    Econometrics, Data Science
  • Location
    Erasmus University Rotterdam, E building, room ET-14
    Rotterdam
  • Date and time

    March 21, 2024
    12:00 - 13:00

Abstract
We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions. First, 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 nonprivate M-estimators. Second, we tackle the problem of parametric inference by constructing differentially private estimators of the asymptotic variance of our private M-estimators. This naturally leads to approximate pivotal statistics for constructing confidence regions and conducting hypothesis testing. We demonstrate the effectiveness of a bias correction that leads to enhanced small-sample empirical performance in simulations. This is joint work with Casey Bradshaw and Po-Ling Loh