arXiv subjects

Amirreza Zamani

Publications and source records attributed to Amirreza Zamani.

At least 19 recordsLinked to original sources

arXiv2026

Sparse Kernel Mechanisms for Locally Differentially Private Discrete Channels

We study sparse locally private discrete mechanisms generated by a nonnegative kernel and an input-dependent admissible output support. The support set is intentionally small relative to the ambient alphabet and acts as a mechanism-design parameter. This formulation covers metric-ball supports, sparse exponential mechanisms, sparse staircase mechanisms, sparse randomized response, sparse additive kernels such as Skellam perturbations, and Poisson-binomial-inspired bounded-support channels. We give a general exact characterization of pure and approximate local differential privacy for this sparse-kernel class. Pure local differential privacy forces all supports to coincide, so genuinely input-dependent sparse supports are incompatible with pure privacy. In the approximate regime, the privacy defect decomposes exactly into support leakage and overlap excess loss. We instantiate the formula for several discrete mechanism families. For sparse staircase mechanisms, a shell-ratio condition eliminates overlap excess loss. For graph-metric supports, overlap of metric balls is necessary for nontrivial privacy. For sparse randomized response, the support-leakage term has a closed form in terms of support mismatch. For generic radius-truncated additive kernels and, in particular, sparse Skellam mechanisms, we obtain exact finite-support formulas in terms of the Skellam CDF and an exact Bessel-ratio overlap condition. Numerical evaluations illustrate how support radius and kernel shape separately affect support leakage and overlap excess loss.

cs.IT↗

arXiv2026

Minimax Quantile Lower Bounds for Interactive Statistical Decision Making with Privacy

Minimax risk and regret are expectation-based criteria and do not capture rare but consequential failures. To address this concern, we develop a $δ$-explicit minimax-quantile theory for interactive statistical decision making (ISDM). We first provide structural relations between minimax quantiles, lower minimax quantiles, and minimax risk. This includes a quantile-to-expectation conversion and an equivalence between strict and lower minimax quantiles outside a countable set of confidence levels. We then derive two converse tools for ISDM: a high-probability interactive Fano's method and a high-probability interactive Le Cam's method. Then, we show that mutual-information (MI) privacy can be handled in the same framework by restricting the admissible decision class. For coordinatewise Gaussian privatization, we derive a two-point template that isolates the privacy-induced variance inflation. We instantiate this template for Gaussian mean estimation, and use the same two-point strategy directly for two-armed Gaussian bandits. We then derive a minimax quantile lower bound for the $K$-armed Gaussian bandit problem, showing that the interactive Fano method captures the exploration cost over multiple possible best arms. The resulting lower bounds are explicit in the confidence level $δ$ and in the privacy budget for the private problems. They yield $\log(1/δ)/n$ scaling for squared-error Gaussian mean estimation, $\sqrt{T\log(1/δ)}$ scaling for two-armed bounded-mean Gaussian bandits, and $\sqrt{KT\log(1/δ)}$-type scaling for the $K$-armed bandits, with privacy appearing through a Gaussian variance-inflation factor for the private problems.

cs.LG↗

arXiv2026

Sparse Discrete Laplace and Gaussian Mechanisms under Local Differential Privacy

We study sparse locally private channels of the form $M(y\mid x)\propto w(x,y) 1\{y\in S(x)\},$ where the admissible output set $S(x)$ is allowed to depend on the private input $x$ and is assumed to be small. Here, we consider the sparse discrete-Laplace family with kernel $w(x,y)=e^{-λd(x,y)}$ and the sparse Gaussian family with kernel $w(x,y)=e^{-d(x,y)^2/(2σ^2)}$. For both families we give exact characterizations of pure and approximate local differential privacy. For pure $\varepsilon$-local differential privacy, we show that input-dependent sparse supports are obtained when all supports coincide. For $(\varepsilon,δ)$-local differential privacy, we derive exact formulas for the privacy defect in terms of support leakage and excess privacy loss on the overlap region. We then specialize the analysis to radius-truncated sparse discrete-Laplace and radius-truncated sparse Gaussian mechanisms and obtain explicit privacy-sparsity tradeoffs in terms of the support size $s$. In particular, we show that nontrivial approximate local privacy requires a minimum support size, whereas larger supports reduce support leakage but increase distortion. For the Gaussian family, the overlap term exhibits an additional quadratic dependence on the support radius, which implies a sharper tradeoff between privacy and sparsity. These results identify the support cardinality as the intrinsic complexity parameter of the mechanism and yield an optimal design principle: choose the smallest support size that satisfies the target privacy constraint.

cs.IT↗

arXiv2026

Sparse Point-wise Privacy Leakage: Mechanism Design and Fundamental Limits

We study an information-theoretic privacy mechanism design problem, where an agent observes useful data $Y$ that is arbitrarily correlated with sensitive data $X$, and design disclosed data $U$ generated from $Y$ (the agent has no direct access to $X$). We introduce \emph{sparse point-wise privacy leakage}, a worst-case privacy criterion that enforces two simultaneous constraints for every disclosed symbol $u\in\mathcal{U}$: (i) $u$ may be correlated with at most $N$ realizations of $X$, and (ii) the total leakage toward those realizations is bounded. In the high-privacy regime, we use concepts from information geometry to obtain a local quadratic approximation of mutual information which measures utility between $U$ and $Y$. When the leakage matrix $P_{X|Y}$ is invertible, this approximation reduces the design problem to a sparse quadratic maximization, known as the Rayleigh-quotient problem, with an $\ell_0$ constraint. We further show that, for the approximated problem, one can without loss of optimality restrict attention to a binary released variable $U$ with a uniform distribution. For small alphabet sizes, the exact sparsity-constrained optimum can be computed via combinatorial support enumeration, which quickly becomes intractable as the dimension grows. For general dimensions, the resulting sparse Rayleigh-quotient maximization is NP-hard and closely related to sparse principal component analysis (PCA). We propose a convex semidefinite programming (SDP) relaxation that is solvable in polynomial time and provides a tractable surrogate for the NP-hard design, together with a simple rounding procedure to recover a feasible leakage direction. We also identify a sparsity threshold beyond which the sparse optimum saturates at the unconstrained spectral value and the SDP relaxation becomes tight.

cs.IT↗

arXiv2026

Privacy-Utility Trade-offs Under Multi-Level Point-Wise Leakage Constraints

An information-theoretic privacy mechanism design is studied, where an agent observes useful data $Y$ which is correlated with the private data $X$. The agent wants to reveal the information to a user, hence, the agent utilizes a privacy mechanism to produce disclosed data $U$ that can be revealed. We assume that the agent has no direct access to $X$, i.e., the private data is hidden. We study privacy mechanism design that maximizes the disclosed information about $Y$, measured by the mutual information between $Y$ and $U$, while satisfying a point-wise constraint with different privacy leakage budgets. We introduce a new measure, called the \emph{multi-level point-wise leakage}, which allows us to impose different leakage levels for different realizations of $U$. In contrast to previous studies on point-wise measures, which use the same leakage level for each realization, we consider a more general scenario in which each data point can leak information up to a different threshold. As a result, this concept also covers cases in which some data points should not leak any information about the private data, i.e., they must satisfy perfect privacy. In other words, a combination of perfect privacy and non-zero leakage can be considered. When the leakage is sufficiently small, concepts from information geometry allow us to locally approximate the mutual information. We show that when the leakage matrix $P_{X|Y}$ is invertible, utilizing this approximation leads to a quadratic optimization problem that has closed-form solution under some constraints. In particular, we show that it is sufficient to consider only binary $U$ to attain the optimal utility. This leads to simple privacy designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix.

cs.IT↗

arXiv2025

An Information Geometric Approach to Fairness With Equalized Odds Constraint

We study the statistical design of a fair mechanism that attains equalized odds, where an agent uses some useful data (database) $X$ to solve a task $T$. Since both $X$ and $T$ are correlated with some latent sensitive attribute $S$, the agent designs a representation $Y$ that satisfies an equalized odds, that is, such that $I(Y;S|T) =0$. In contrast to our previous work, we assume here that the agent has no direct access to $S$ and $T$; hence, the Markov chains $S - X - Y$ and $T - X - Y$ hold. Furthermore, we impose a geometric structure on the conditional distribution $P_{S|Y}$, allowing $Y$ and $S$ to have a small correlation, bounded by a threshold. When the threshold is small, concepts from information geometry allow us to approximate mutual information and reformulate the fair mechanism design problem as a quadratic program with closed-form solutions under certain constraints. For other cases, we derive simple, low-complexity lower bounds based on the maximum singular value and vector of a matrix. Finally, we compare our designs with the optimal solution in a numerical example.

cs.IT↗

arXiv2025

On Information Theoretic Fairness With A Bounded Point-Wise Statistical Parity Constraint: An Information Geometric Approach

In this paper, we study an information-theoretic problem of designing a fair representation under a bounded point-wise statistical (demographic) parity constraint. More specifically, an agent uses some useful data (database) $X$ to solve a task $T$. Since both $X$ and $T$ are correlated with some latent sensitive attribute or secret $S$, the agent designs a representation $Y$ that satisfies a bounded point-wise statistical parity, that is, such that for all realizations of the representation $y\in\cal Y$, we have $χ^2(P_{S|y};P_S)\leq ε$. In contrast to our previous work, here we use the point-wise measure instead of a bounded mutual information, and we assume that the agent has no direct access to $S$ and $T$; hence, the Markov chains $S - X - Y$ and $T - X - Y$ hold. In this work, we design $Y$ that maximizes the mutual information $I(Y;T)$ about the task while satisfying a bounded compression rate constraint, that is, ensuring that $I(Y;X) \leq r$. Finally, $Y$ satisfies the point-wise bounded statistical parity constraint $χ^2(P_{S|y};P_S)\leq ε$. When $ε$ is small, concepts from information geometry allow us to locally approximate the KL-divergence and mutual information. To design the representation $Y$, we utilize this approximation and show that the main complex fairness design problem can be rewritten as a quadratic optimization problem that has simple closed-form solution under certain constraints. For the cases where the closed-form solution is not obtained we obtain lower bounds with low computational complexity. Here, we provide simple fairness designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix. Finally, in a numerical example we compare our obtained results with the optimal solution.

cs.IT↗

arXiv2025

Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making

Minimax risk and regret focus on expectation, missing rare failures critical in safety-critical bandits and reinforcement learning. Minimax quantiles capture these tails. Three strands of prior work motivate this study: minimax-quantile bounds restricted to non-interactive estimation; unified interactive analyses that focus on expected risk rather than risk level specific quantile bounds; and high-probability bandit bounds that still lack a quantile-specific toolkit for general interactive protocols. To close this gap, within the interactive statistical decision making framework, we develop high-probability Fano and Le Cam tools and derive risk level explicit minimax-quantile bounds, including a quantile-to-expectation conversion and a tight link between strict and lower minimax quantiles. Instantiating these results for the two-armed Gaussian bandit immediately recovers optimal-rate bounds.

cs.IT↗

arXiv2025

Information-Theoretic Fairness with A Bounded Statistical Parity Constraint

In this paper, we study an information-theoretic problem of designing a fair representation that attains bounded statistical (demographic) parity. More specifically, an agent uses some useful data $X$ to solve a task $T$. Since both $X$ and $T$ are correlated with some sensitive attribute or secret $S$, the agent designs a representation $Y$ that satisfies a bounded statistical parity and/or privacy leakage constraint, that is, such that $I(Y;S) \leq ε$. Here, we relax the perfect demographic (statistical) parity and consider a bounded-parity constraint. In this work, we design the representation $Y$ that maximizes the mutual information $I(Y;T)$ about the task while satisfying a bounded compression (or encoding rate) constraint, that is, ensuring that $I(Y;X) \leq r$. Simultaneously, $Y$ satisfies the bounded statistical parity constraint $I(Y;S) \leq ε$. To design $Y$, we use extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma which are based on randomization techniques and study the tightness of the obtained bounds in special cases. The main idea to derive the lower bounds is to use randomization over useful data $X$ or sensitive data $S$. Considering perfect demographic parity, i.e., $ε=0$, we improve the existing results (lower bounds) by using a tighter version of the Strong Functional Representation Lemma and propose new upper bounds. We then propose upper and lower bounds for the main problem and show that allowing non-zero leakage can improve the attained utility. Finally, we study the bounds and compare them in a numerical example. The problem studied in this paper can also be interpreted as one of code design with bounded leakage and bounded rate privacy considering the sensitive attribute as a secret.

cs.IT↗

arXiv2025

Cache-Aided Variable-Length Coding with Perfect Privacy

A cache-aided compression problem with perfect privacy is studied, where a server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits. The server is connected to $K$ users through a shared link, where each user has access to a local cache of size $MF$ bits. In the placement phase, the server fills the users$'$ caches without prior knowledge of their future demands, while the delivery phase takes place after the users send their demands to the server. We assume that each file $Y_i$ is arbitrarily correlated with a private attribute $X$, and an adversary is assumed to have access to the shared link. The users and the server have access to a shared secret key $W$. The goal is to design the cache contents and the delivered message $\cal C$ such that the average length of $\mathcal{C}$ is minimized, while satisfying: i. The response $\cal C$ does not disclose any information about $X$, i.e., $X$ and $\cal C$ are statistically independent yielding $I(X;\mathcal{C})=0$, which corresponds to the perfect privacy constraint; ii. User $i$ is able to decode its demand, $Y_{d_i}$, by using its local cache $Z_i$, delivered message $\cal C$, and the shared secret key $W$. Due to the correlation of database with the private attribute, existing codes for cache-aided delivery do not fulfill the perfect privacy constraint. Indeed, in this work, we propose a lossless variable-length coding scheme that combines privacy-aware compression with coded caching techniques. In particular, we use two-part code construction and Functional Representation Lemma. Furthermore, we propose an alternative coding scheme based on the minimum entropy coupling concept and a greedy entropy-based algorithm. We show that the proposed scheme improves the previous results obtained by Functional Representation Lemma.

cs.IT↗

arXiv2025

An Information Geometric Approach to Local Information Privacy with Applications to Max-lift and Local Differential Privacy

We study an information-theoretic privacy mechanism design, where an agent observes useful data $Y$ and wants to reveal the information to a user. Since the useful data is correlated with the private data $X$, the agent uses a privacy mechanism to produce disclosed data $U$ that can be released. We assume that the agent observes $Y$ and has no direct access to $X$, i.e., the private data is hidden. We study the privacy mechanism design that maximizes the revealed information about $Y$ while satisfying a bounded Local Information Privacy (LIP) criterion. When the leakage is sufficiently small, concepts from information geometry allow us to locally approximate the mutual information. By utilizing this approximation the main privacy-utility trade-off problem can be rewritten as a quadratic optimization problem that has closed-form solution under some constraints. For the cases where the closed-form solution is not obtained we provide lower bounds on it. In contrast to the previous works that have complexity issues, here, we provide simple privacy designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix. To do so, we follow two approaches where in the first one we find a lower bound on the main problem and then approximate it, however, in the second approach we approximate the main problem directly. In this work, we present geometrical interpretations of the proposed methods and in a numerical example we compare our results considering both approaches with the optimal solution and the previous methods. Furthermore, we discuss how our method can be generalized considering larger amounts for the privacy leakage. Finally, we discuss how the proposed methods can be applied to deal with differential privacy.

cs.IT↗

arXiv2024

Near-Field ISAC in 6G: Addressing Phase Nonlinearity via Lifted Super-Resolution

Integrated sensing and communications (ISAC) is a promising component of 6G networks, fusing communication and radar technologies to facilitate new services. Additionally, the use of extremely large-scale antenna arrays (ELAA) at the ISAC common receiver not only facilitates terahertz-rate communication links but also significantly enhances the accuracy of target detection in radar applications. In practical scenarios, communication scatterers and radar targets often reside in close proximity to the ISAC receiver. This, combined with the use of ELAA, fundamentally alters the electromagnetic characteristics of wireless and radar channels, shifting from far-field planar-wave propagation to near-field spherical wave propagation. Under the far-field planar-wave model, the phase of the array response vector varies linearly with the antenna index. In contrast, in the near-field spherical wave model, this phase relationship becomes nonlinear. This shift presents a fundamental challenge: the widely-used Fourier analysis can no longer be directly applied for target detection and communication channel estimation at the ISAC common receiver. In this work, we propose a feasible solution to address this fundamental issue. Specifically, we demonstrate that there exists a high-dimensional space in which the phase nonlinearity can be expressed as linear. Leveraging this insight, we develop a lifted super-resolution framework that simultaneously performs communication channel estimation and extracts target parameters with high precision.

eess.SP↗

arXiv2024

Private Semantic Communications with Separate Blind Encoders

We study a semantic communication problem with a privacy constraint where an encoder consists of two separate parts, e.g., encoder 1 and encoder 2. The first encoder has access to information source $X=(X_1,\ldots,X_N)$ which is arbitrarily correlated with private data $S$. The private data is not accessible by encoder 1, however, the second encoder has access to it and the output of encoder 1. A user asks for a task $h(X)$ and the first encoder designs the semantic of the information source $f(X)$ to disclose. Due to the privacy constraints $f(X)$ can not be revealed directly to the user and the second encoder applies a statistical privacy mechanism to produce disclosed data $U$. Here, we assume that encoder 2 has no access to the task and the design of the disclosed data is based on the semantic and the private data. In this work, we propose a novel approach where $U$ is produced by solving a privacy-utility trade-off based on the semantic and the private data. We design $U$ utilizing different methods such as using extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma. We evaluate our design by computing the utility attained by the user. Finally, we study and compare the obtained bounds in a numerical example.

cs.IT↗

arXiv2024

Extended Functional Representation Lemma: A Tool For Privacy, Semantic Representation, Caching, and Compression Design

This paper provides an overview of a problem in information-theoretic privacy mechanism design, addressing two scenarios in which private data is either observable or hidden. In each scenario, different privacy measures are used, including bounded mutual information and two types of per-letter privacy constraints. Considering the first scenario, an agent observes useful data that is correlated with private data, and wants to disclose the useful information to a user. Due to the privacy concerns, direct disclosure is prohibited. Hence, a privacy mechanism is designed to generate disclosed data which maximizes the revealed information about the useful data while satisfying a privacy constraint. In the second scenario, the agent has additionally access to the private data. We discuss how the Functional Representation Lemma, the Strong Functional Representation Lemma, and their extended versions are useful for designing low-complexity privacy mechanisms that achieve optimal privacy-utility trade-offs under certain constraints. Furthermore, another privacy design problem is presented where part of the private attribute is more private than the remaining part. Finally, we provide applications including semantic communications, caching and delivery, and compression designs, where the approach can be applied.

cs.IT↗

arXiv2024

Improving Achievability of Cache-Aided Private Variable-Length Coding with Zero Leakage

A statistical cache-aided compression problem with a privacy constraint is studied, where a server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is linked through a shared channel to $K$ users, where each has access to a local cache memory of size $MF$ bits. During the placement phase, the server fills the users' caches without prior knowledge of their demands, while the delivery phase takes place after the users send their demands to the server. We assume that each file in database $Y_i$ is arbitrarily correlated with a private attribute $X$, and an adversary is assumed to have access to the shared channel. The users and the server have access to a shared key $W$. The goal is to design the cache contents and the delivered message $\cal C$ such that the average length of $\mathcal{C}$ is minimized, while satisfying: i. The response $\cal C$ does not reveal any information about $X$, i.e., $I(X;\mathcal{C})=0$; ii. User $i$ can decode its demand, $Y_{d_i}$, by using the shared key $W$, $\cal C$, and its local cache $Z_i$. In a previous work, we have proposed a variable-length coding scheme that combines privacy-aware compression with coded caching techniques. In this paper, we propose a new achievability scheme using minimum entropy coupling concept and a greedy entropy-based algorithm. We show that the proposed scheme improves the previous results. Moreover, considering two special cases we improve the obtained bounds using the common information concept.

cs.IT↗

arXiv2024

On Information Theoretic Fairness: Compressed Representations With Perfect Demographic Parity

In this article, we study the fundamental limits in the design of fair and/or private representations achieving perfect demographic parity and/or perfect privacy through the lens of information theory. More precisely, given some useful data $X$ that we wish to employ to solve a task $T$, we consider the design of a representation $Y$ that has no information of some sensitive attribute or secret $S$, that is, such that $I(Y;S) = 0$. We consider two scenarios. First, we consider a design desiderata where we want to maximize the information $I(Y;T)$ that the representation contains about the task, while constraining the level of compression (or encoding rate), that is, ensuring that $I(Y;X) \leq r$. Second, inspired by the Conditional Fairness Bottleneck problem, we consider a design desiderata where we want to maximize the information $I(Y;T|S)$ that the representation contains about the task which is not shared by the sensitive attribute or secret, while constraining the amount of irrelevant information, that is, ensuring that $I(Y;X|T,S) \leq r$. In both cases, we employ extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma and study the tightness of the obtained bounds. Every result here can also be interpreted as a coding with perfect privacy problem by considering the sensitive attribute as a secret.

cs.IT↗

arXiv2024

Multi-Task Private Semantic Communication

We study a multi-task private semantic communication problem, in which an encoder has access to an information source arbitrarily correlated with some latent private data. A user has $L$ tasks with priorities. The encoder designs a message to be revealed which is called the semantic of the information source. Due to the privacy constraints the semantic can not be disclosed directly and the encoder adds noise to produce disclosed data. The goal is to design the disclosed data that maximizes the weighted sum of the utilities achieved by the user while satisfying a privacy constraint on the private data. In this work, we first consider a single-task scenario and design the added noise utilizing various methods including the extended versions of the Functional Representation Lemma, Strong Functional Representation Lemma, and separation technique. We then study the multi-task scenario and derive a simple design of the source semantics. We show that in the multi-task scenario the main problem can be divided into multiple parallel single-task problems.

cs.IT↗

arXiv2023

Private Variable-Length Coding with Non-zero Leakage

A private compression design problem is studied, where an encoder observes useful data $Y$, wishes to compress it using variable length code and communicates it through an unsecured channel. Since $Y$ is correlated with private data $X$, the encoder uses a private compression mechanism to design encoded message $\cal C$ and sends it over the channel. An adversary is assumed to have access to the output of the encoder, i.e., $\cal C$, and tries to estimate $X$. Furthermore, it is assumed that both encoder and decoder have access to a shared secret key $W$. In this work, we generalize the perfect privacy (secrecy) assumption and consider a non-zero leakage between the private data $X$ and encoded message $\cal C$. The design goal is to encode message $\cal C$ with minimum possible average length that satisfies non-perfect privacy constraints. We find upper and lower bounds on the average length of the encoded message using different privacy metrics and study them in special cases. For the achievability we use two-part construction coding and extended versions of Functional Representation Lemma. Lastly, in an example we show that the bounds can be asymptotically tight.

cs.IT↗