arXiv subjects

Mohammad Amin Zarrabian

Publications and source records attributed to Mohammad Amin Zarrabian.

10 recordsLinked to original sources

arXiv2026

On Privacy Mechanism Design Under a Bounded $α$-Lift Leakage Constraint with $χ^2$-Utility

We study the design of a statistical privacy mechanism under a bounded $α$-lift leakage constraint. An agent observes useful data $Y$, which is arbitrarily correlated with private data $X$, and releases $U$. The goal is to maximize Pearson $χ^2$-information $χ^2(Y;U)$ while satisfying the point-wise privacy constraint. This utility is an $f$-information that is nonnegative, obeys data processing, and measures the aggregate normalized change from the prior $P_Y$ to the posteriors $P_{Y|U=u}$. The main benefit of this choice is that $χ^2(Y;U)$ is exactly quadratic in the posterior perturbations; hence, no local approximation of the utility is required. For the nonlinear $α$-lift constraint, we derive a uniform Taylor-remainder bound that remains valid for the optimizing, $ε$-dependent perturbation. When $P_{X|Y}$ is invertible, this yields a closed-form quadratic surrogate, an explicitly scaled binary mechanism that satisfies the original $α$-lift constraint, a computable sufficient range for $ε$, and an $O(ε^{3/2})$ bound on the utility gap. For $α=2$, the solution is exact over an explicit range. We transfer these results to point-wise Rényi-divergence privacy, including an exact-feasible mechanism, an explicit privacy-budget range, and matching gap bounds. We also give an exact formulation for arbitrary leakage matrices and evaluate exact-feasible mechanisms numerically.

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arXiv2025

An Extension of the Adversarial Threat Model in Quantitative Information Flow

In this paper, we propose an extended framework for quantitative information flow (QIF), aligned with the previously proposed core-concave generalization of entropy measures, to include adversaries that use Kolmogorov-Nagumo $f$-mean to infer secrets in a private system. Specifically, in our setting, an adversary uses Kolmogorov-Nagumo $f$-mean to compute its best actions before and after observing the system's randomized outputs. This leads to generalized notions of prior and posterior vulnerability and generalized axiomatic relations that we will derive to elucidate how these $f$-mean based vulnerabilities interact with each other. We demonstrate the usefulness of this framework by showing how some notions of leakage that had been derived outside of the QIF framework and so far seemed incompatible with it are indeed explainable via such an extension of QIF. These leakage measures include $α$-leakage, which is the same as Arimoto mutual information of order $α$, maximal $α$-leakage, which is the $α$-leakage capacity, and maximal $(α,β)$-leakage, which is a generalization of the above and captures local differential privacy as a special case. We define the notion of generalized capacity and provide partial results for special classes of functions used in the Kolmogorov-Nagumo mean. We also propose a new pointwise notion of gain function, which we coin pointwise information gain. We show that this pointwise information gain can explain R{é}yni divergence and Sibson mutual information of order $α\in [0,\infty]$ as the Kolmogorov-Nagumo average of the gain with a proper choice of function $f$.

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arXiv2024

An Algorithm for Enhancing Privacy-Utility Tradeoff in the Privacy Funnel and Other Lift-based Measures

This paper investigates the privacy funnel, a privacy-utility tradeoff problem in which mutual information quantifies both privacy and utility. The objective is to maximize utility while adhering to a specified privacy budget. However, the privacy funnel represents a non-convex optimization problem, making it challenging to achieve an optimal solution. An existing proposed approach to this problem involves substituting the mutual information with the lift (the exponent of information density) and then solving the optimization. Since mutual information is the expectation of the information density, this substitution overestimates the privacy loss and results in a final smaller bound on the privacy of mutual information than what is allowed in the budget. This significantly compromises the utility. To overcome this limitation, we propose using a privacy measure that is more relaxed than the lift but stricter than mutual information while still allowing the optimization to be efficiently solved. Instead of directly using information density, our proposed measure is the average of information density over the sensitive data distribution for each observed data realization. We then introduce a heuristic algorithm capable of achieving solutions that produce extreme privacy values, which enhances utility. The numerical results confirm improved utility at the same privacy budget compared to existing solutions in the literature. Additionally, we explore two other privacy measures, $\ell_{1}$-norm and strong $χ^2$-divergence, demonstrating the applicability of our algorithm to these lift-based measures. We evaluate the performance of our method by comparing its output with previous works. Finally, we validate our heuristic approach with a theoretical framework that estimates the optimal utility for strong $χ^2$-divergence, numerically showing a perfect match.

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arXiv2024

$α$-leakage by Rényi Divergence and Sibson Mutual Information

For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, this paper proposes a $\tilde{f}$-mean information gain measure. Rényi divergence is shown to be the maximum $\tilde{f}$-mean information gain incurred at each elementary event $y$ of channel output $Y$ and Sibson mutual information is the $\tilde{f}$-mean of this $Y$-elementary information gain. Both are proposed as $α$-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing $α$-leakage by Arimoto mutual information can be expressed as $\tilde{f}$-mean measures by a scaled probability. Further, Sibson mutual information is interpreted as the maximum $\tilde{f}$-mean information gain over all estimation decisions applied to channel output.

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arXiv2024

Privacy-Utility Tradeoff Based on $α$-lift

Information density and its exponential form, known as lift, play a central role in information privacy leakage measures. $α$-lift is the power-mean of lift, which is tunable between the worst-case measure max-lift ($α=\infty$) and more relaxed versions ($α<\infty$). This paper investigates the optimization problem of the privacy-utility tradeoff (PUT) where $α$-lift and mutual information are privacy and utility measures, respectively. Due to the nonlinear nature of $α$-lift for $α<\infty$, finding the optimal solution is challenging. Therefore, we propose a heuristic algorithm to estimate the optimal utility for each value of $α$, inspired by the optimal solution for $α=\infty$ and the convexity of $α$-lift with respect to the lift, which we prove. The numerical results show the efficacy of the algorithm and indicate the effective range of $α$ and privacy budget $\varepsilon$ with good PUT performance.

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arXiv2024

A Cross Entropy Interpretation of R{é}nyi Entropy for $α$-leakage

This paper proposes an $α$-leakage measure for $α\in[0,\infty)$ by a cross entropy interpretation of R{é}nyi entropy. While Rényi entropy was originally defined as an $f$-mean for $f(t) = \exp((1-α)t)$, we reveal that it is also a $\tilde{f}$-mean cross entropy measure for $\tilde{f}(t) = \exp(\frac{1-α}αt)$. Minimizing this Rényi cross-entropy gives Rényi entropy, by which the prior and posterior uncertainty measures are defined corresponding to the adversary's knowledge gain on sensitive attribute before and after data release, respectively. The $α$-leakage is proposed as the difference between $\tilde{f}$-mean prior and posterior uncertainty measures, which is exactly the Arimoto mutual information. This not only extends the existing $α$-leakage from $α\in [1,\infty)$ to the overall R{é}nyi order range $α\in [0,\infty)$ in a well-founded way with $α=0$ referring to nonstochastic leakage, but also reveals that the existing maximal leakage is a $\tilde{f}$-mean of an elementary $α$-leakage for all $α\in [0,\infty)$, which generalizes the existing pointwise maximal leakage.

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arXiv2023

On the Lift, Related Privacy Measures, and Applications to Privacy-Utility Tradeoffs

This paper investigates lift, the likelihood ratio between the posterior and prior belief about sensitive features in a dataset. Maximum and minimum lifts over sensitive features quantify the adversary's knowledge gain and should be bounded to protect privacy. We demonstrate that max and min lifts have a distinct range of values and probability of appearance in the dataset, referred to as \emph{lift asymmetry}. We propose asymmetric local information privacy (ALIP) as a compatible privacy notion with lift asymmetry, where different bounds can be applied to min and max lifts. We use ALIP in the watchdog and optimal random response (ORR) mechanisms, the main methods to achieve lift-based privacy. It is shown that ALIP enhances utility in these methods compared to existing local information privacy, which ensures the same (symmetric) bounds on both max and min lifts. We propose subset merging for the watchdog mechanism to improve data utility and subset random response for the ORR to reduce complexity. We then investigate the related lift-based measures, including $\ell_1$-norm, $χ^2$-privacy criterion, and $α$-lift. We reveal that they can only restrict max-lift, resulting in significant min-lift leakage. To overcome this problem, we propose corresponding lift-inverse measures to restrict the min-lift. We apply these lift-based and lift-inverse measures in the watchdog mechanism. We show that they can be considered as relaxations of ALIP, where a higher utility can be achieved by bounding only average max and min lifts.

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arXiv2022

Asymmetric Local Information Privacy and the Watchdog Mechanism

This paper proposes a novel watchdog privatization scheme by generalizing local information privacy (LIP) to enhance data utility. To protect the sensitive features $S$ correlated with some useful data $X$, LIP restricts the lift, the ratio of the posterior belief to the prior on $S$ after and before accessing $X$. For each $x$, both maximum and minimum lift over sensitive features are measures of the privacy risk of publishing this symbol and should be restricted for the privacy-preserving purpose. Previous works enforce the same bound for both max-lift and min-lift. However, empirical observations show that the min-lift is usually much smaller than the max-lift. In this work, we generalize the LIP definition to consider the unequal values of max and min lift, i.e., considering different bounds for max-lift and min-lift. This new definition is applied to the watchdog privacy mechanism. We demonstrate that the utility is enhanced under a given privacy constraint on local differential privacy. At the same time, the resulting max-lift is lower and, therefore, tightly restricts other privacy leakages, e.g., mutual information, maximal leakage, and $α$-leakage.

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arXiv2021

Enhancing Utility in the Watchdog Privacy Mechanism

This paper is concerned with enhancing data utility in the privacy watchdog method for attaining information-theoretic privacy. For a specific privacy constraint, the watchdog method filters out the high-risk data symbols through applying a uniform data regulation scheme, e.g., merging all high-risk symbols together. While this method entirely trades the symbols resolution off for privacy, we show that the data utility can be greatly improved by partitioning the high-risk symbols set and individually privatizing each subset. We further propose an agglomerative merging algorithm that finds a suitable partition of high-risk symbols: it starts with a singleton high-risk symbol, which is iteratively fused with others until the resulting subsets are private.~Numerical simulations demonstrate the efficacy of this algorithm in privately achieving higher utilities in the watchdog scheme.

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arXiv2021

$α$-Information-theoretic Privacy Watchdog and Optimal Privatization Scheme

This paper proposes an $α$-lift measure for data privacy and determines the optimal privatization scheme that minimizes the $α$-lift in the watchdog method. To release data $X$ that is correlated with sensitive information $S$, the ratio $l(s,x) = \frac{p(s|x)}{p(s)} $ denotes the `lift' of the posterior belief on $S$ and quantifies data privacy. The $α$-lift is proposed as the $L_α$-norm of the lift: $\ell_α(x) = \| (\cdot,x) \|_α = (E[l(S,x)^α])^{1/α}$. This is a tunable measure: When $α< \infty$, each lift is weighted by its likelihood of appearing in the dataset (w.r.t. the marginal probability $p(s)$); For $α= \infty$, $α$-lift reduces to the existing maximum lift. To generate the sanitized data $Y$, we adopt the privacy watchdog method using $α$-lift: Obtain $\mathcal{X}_ε$ containing all $x$'s such that $\ell_α(x) > e^ε$; Apply the randomization $r(y|x)$ to all $x \in \mathcal{X}_ε$, while all other $x \in \mathcal{X} \setminus \mathcal{X}_ε$ are published directly. For the resulting $α$-lift $\ell_α(y)$, it is shown that the Sibson mutual information $I_α^{S}(S;Y)$ is proportional to $E[ \ell_α(y)]$. We further define a stronger measure $\bar{I}_α^{S}(S;Y)$ using the worst-case $α$-lift: $\max_{y} \ell_α(y)$. We prove that the optimal randomization $r^*(y|x)$ that minimizes both $I_α^{S}(S;Y)$ and $\bar{I}_α^{S}(S;Y)$ is $X$-invariant, i.e., $r^*(y|x) = R(y), \forall x\in \mathcal{X}_ε$ for any probability distribution $R$ over $y \in \mathcal{X}_ε$. Numerical experiments show that $α$-lift can provide flexibility in the privacy-utility tradeoff.

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