[Turkmath:6750] Galatasaray Üniversitesi Seminer Duyurusu - Sinan Yıldırım (Sabancı) - 20.11.24

[Galatasaray Üniversitesi Matematik Seminerleri]

*Speaker:* Sinan Yildirim (Sabancı Üniversitesi)
*Date:* 10.11.2024
*Time:* 15:00 - 16:00
*Location:* Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 
Beşiktaş,H 306


*Title: Adaptive Online Bayesian Estimation of Frequency Distributions 
with Local Differential Privacy *

*Abstract:* We propose a novel Bayesian approach for the adaptive and 
online estimation of the frequency distribution of a finite number of 
categories under the local differential privacy (LDP) framework. The 
proposed algorithm performs Bayesian parameter estimation via posterior 
sampling and adapts the randomization mechanism for LDP based on the 
obtained posterior samples. We propose a randomized mechanism for LDP 
which uses a subset of categories as an input and whose performance 
depends on the selected subset and the true frequency distribution. By 
using the posterior sample as an estimate of the frequency distribution, 
the algorithm performs a computationally tractable subset selection step 
to maximize the utility of the privatized response of the next user. We 
propose several utility functions related to well-known information 
metrics, such as (but not limited to) Fisher information matrix, total 
variation distance, and information entropy. We compare each of these 
utility metrics in terms of their computational complexity. We employ 
stochastic gradient Langevin dynamics for posterior sampling, a 
computationally efficient approximate Markov chain Monte Carlo method. 
We provide a theoretical analysis showing that (i) the posterior 
distribution targeted by the algorithm converges to the true parameter 
even for approximate posterior sampling, and (ii) the algorithm selects 
the optimal subset with high probability if posterior sampling is 
performed exactly. We also provide numerical results that empirically 
demonstrate the estimation accuracy of our algorithm where we compare it 
with non-adaptive and semi-adaptive approaches under experimental 
settings with various combinations of privacy parameters and population 
distribution parameters.

*(joint w. Soner Aydın)*


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Galatasaray Üniversitesi Matematik Bölümü

https://matematik.gsu.edu.tr/tr/arastirma/seminerler

<https://matematik.gsu.edu.tr/>



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