arXiv subjects

Ehab ElSalamouny

Publications and source records attributed to Ehab ElSalamouny.

6 recordsLinked to original sources

arXiv2026

On the Consistency and Performance of the Iterative Bayesian Update

In many situations, estimating the distribution of users' data concerning certain attributes is important. To facilitate this estimation while safeguarding users' privacy, the local privacy model is commonly employed, in which each user applies a local protection mechanism to release a noisy version of their original data to the data collector. The original distribution is then estimated using methods such as Matrix Inversion (INV), RAPPOR's estimator, and iterative Bayesian update (IBU). In this article, we experimentally demonstrate that IBU significantly outperforms the other methods when user data is protected through metric privacy mechanisms. We also explain the mathematical reason for the suboptimal performance of INV under those metric privacy mechanisms. Conversely, IBU exhibits performance similar to INV under typical mechanisms of local differential privacy, specifically the k-RR and RAPPOR. In addition, we investigate IBU's consistency, which is a crucial property as it means that the estimate converges to the true distribution as the number of data points increases. In the literature, IBU is claimed to be consistent, but there is no proof for this claim. We provide a formal proof of consistency leveraging the fact that IBU is a maximum likelihood estimator. Finally, we examine scenarios involving an infinite alphabet for sensitive data and propose a method allowing IBU to operate effectively in these situations.

cs.CR↗

arXiv2026

Estimating the True Distribution of Data Collected with Randomized Response

Randomized Response (RR) is a protocol designed to collect and analyze categorical data with local differential privacy guarantees. It has been used as a building block of mechanisms deployed by Big tech companies to collect app or web users' data. Each user reports an automatic random alteration of their true value to the analytics server, which then estimates the histogram of the true unseen values of all users using a debiasing rule to compensate for the added randomness. A known issue is that the standard debiasing rule can yield a vector with negative values (which can not be interpreted as a histogram), and there is no consensus on the best fix. An elegant but slow solution is the Iterative Bayesian Update algorithm (IBU), which converges to the Maximum Likelihood Estimate (MLE) as the number of iterations goes to infinity. This paper bypasses IBU by providing a simple formula for the exact MLE of RR and compares it with other estimation methods experimentally to help practitioners decide which one to use.

cs.CR↗

arXiv2022

Reconstruction of the distribution of sensitive data under free-will privacy

The local privacy mechanisms, such as k-RR, RAPPOR, and the geo-indistinguishability ones, have become quite popular thanks to the fact that the obfuscation can be effectuated at the users end, thus avoiding the need of a trusted third party. Another important advantage is that each data point is sanitized independently from the others, and therefore different users may use different levels of obfuscation depending on their privacy requirements, or they may even use entirely different mechanisms depending on the services they are trading their data for. A challenging requirement in this setting is to construct the original distribution on the users sensitive data from their noisy versions. Existing techniques can only estimate that distribution separately on each obfuscation schema and corresponding noisy data subset. But the smaller are the subsets, the more imprecise the estimations are. In this paper we study how to avoid the subsets-fractioning problem when combining local privacy mechanisms, thus recovering an optimal utility. We focus on the estimation of the original distribution, and on the two main methods to estimate it: the matrix-inversion method and the iterative Bayes update. We consider various cases of combination of local privacy mechanisms, and compare the flexibility and the performance of the two methods.

cs.CR↗

arXiv2019

Full Convergence of the Iterative Bayesian Update and Applications to Mechanisms for Privacy Protection

The iterative Bayesian update (IBU) and the matrix inversion (INV) are the main methods to retrieve the original distribution from noisy data resulting from the application of privacy protection mechanisms. We show that the theoretical foundations of the IBU established in the literature are flawed, as they rely on an assumption that in general is not satisfied in typical real datasets. We then fix the theory of the IBU, by providing a general convergence result for the underlying Expectation-Maximization method. Our framework does not rely on the above assumption, and also covers a more general local privacy model. Finally we evaluate the precision of the IBU on data sanitized with the Geometric, $k$-RR, and RAPPOR mechanisms, and we show that it outperforms INV in the first case, while it is comparable to INV in the other two cases.

cs.CR↗

arXiv2018

Optimal noise functions for location privacy on continuous regions

Users of location-based services (LBSs) are highly vulnerable to privacy risks since they need to disclose, at least partially, their locations to benefit from these services. One possibility to limit these risks is to obfuscate the location of a user by adding random noise drawn from a noise function. In this paper, we require the noise functions to satisfy a generic location privacy notion called $\ell$-privacy, which makes the position of the user in a given region $\mathcal{X}$ relatively indistinguishable from other points in $\mathcal{X}$. We also aim at minimizing the loss in the service utility due to such obfuscation. While existing optimization frameworks regard the region $\mathcal{X}$ restrictively as a finite set of points, we consider the more realistic case in which the region is rather continuous with a non-zero area. In this situation, we demonstrate that circular noise functions are enough to satisfy $\ell$-privacy on $\mathcal{X}$ and equivalently on the entire space without any penalty in the utility. Afterwards, we describe a large parametric space of noise functions that satisfy $\ell$-privacy on $\mathcal{X}$, and show that this space has always an optimal member, regardless of $\ell$ and $\mathcal{X}$. We also investigate the recent notion of $ε$-geo-indistinguishability as an instance of $\ell$-privacy, and prove in this case that with respect to any increasing loss function, the planar Laplace noise function is optimal for any region having a nonzero area.

cs.CR↗

arXiv2015

Improving the Performance of Multi-class Intrusion Detection Systems using Feature Reduction

Intrusion detection systems (IDS) are widely studied by researchers nowadays due to the dramatic growth in network-based technologies. Policy violations and unauthorized access is in turn increasing which makes intrusion detection systems of great importance. Existing approaches to improve intrusion detection systems focus on feature selection or reduction since some features are irrelevant or redundant which when removed improve the accuracy as well as the learning time. In this paper we propose a hybrid feature selection method using Correlation-based Feature Selection and Information Gain. In our work we apply adaptive boosting using naïve Bayes as the weak (base) classifier. The key point in our research is that we are able to improve the detection accuracy with a reduced number of features while precisely determining the attack. Experimental results showed that our proposed method achieved high accuracy compared to methods using only 5-class problem. Correlation is done using Greedy search strategy and naïve Bayes as the classifier on the reduced NSL-KDD dataset.

cs.NI↗