[Statlist] Research Seminar in Statistics *FRIDAY, 17 December 2021* GSEM, University of Geneva

[gsem-support-instituts]

Due to new measures decided by the Federal Council, all public events organized by the UNIGE are subject to the compulsory presentation of the COVID


Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you


Organized by Prof. Sebastian Engelke on behalf of the Research Center for Statistics (https://www.unige.ch/gsem/en/research/institutes/rcs/)


FRIDAY, 17 DECEMBER 2021 at 11:15am, Uni-Mail M 5220 & ONLINE

Zoom research webinar: https://unige.zoom.us/j/92924332087?pwd=U1U1NFk4dTFCRHBMeWYrSDBQcXBiQT09
Meeting ID: 929 2433 2087
Passcode: 399192


Differentially Private Inference via Noisy Optimization
(Joint with Casey Bradshaw and Po-Ling Loh)
Marco AVELLA MEDINA, Columbia University, USA, http://stat.columbia.edu/department-directory/name/marco-avella/

ABSTRACT:
We propose a general optimization-based framework for computing differentially private M-estimators and a new method for the construction of differentially private confidence regions. Firstly, we show that robust statistics can be used in conjunction with noisy gradient descent and noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively. We establish global convergence guarantees, under both local strong convexity and self-concordance, showing that our private estimators converge with high probability to a neighborhood of the non-private M-estimators. The radius of this neighborhood is nearly optimal in the sense it corresponds to the statistical minimax cost of differential privacy up to a logarithmic term. Secondly, 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 the use of approximate pivotal statistics for the construction of confidence regions and hypothesis testing. We demonstrate the effectiveness of a bias correction that leads to enhanced small-sample empirical performance in simulations.


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