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*Speaker:* Sinan Yildirim (Sabancı Üniversitesi)<br>
*Date:* 10.11.2024<br>
*Time:* 15:00 - 16:00<br>
*Location:* Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36,
34349 Beşiktaş,H 306<br>
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*Title: Adaptive Online Bayesian Estimation of Frequency
Distributions with Local Differential Privacy *<br>
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*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.<br>
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*(joint w. Soner Aydın)*<br>
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* To access to the complete seminar calendar please visit this link<br>
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Galatasaray Üniversitesi Matematik Bölümü<br>
<br>
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