arXiv subjects

Amirreza Zamani

Publications and source records attributed to Amirreza Zamani.

30 records · Page 2Linked to original sources

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.

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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.

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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.

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arXiv2023

Private Variable-Length Coding with 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 attribute $X$, 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 $W$. The design goal is to encode message $\cal C$ with minimum possible average length that satisfies a perfect privacy constraint. To do so we first consider two different privacy mechanism design problems and find upper bounds on the entropy of the optimizers by solving a linear program. We use the obtained optimizers to design $\cal C$. In two cases we strengthen the existing bounds: 1. $|\mathcal{X}|\geq |\mathcal{Y}|$; 2. The realization of $(X,Y)$ follows a specific joint distribution. In particular, considering the second case we use two-part construction coding to achieve the upper bounds. Furthermore, in a numerical example we study the obtained bounds and show that they can improve the existing results.

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arXiv2023

New Privacy Mechanism Design With Direct Access to the Private Data

The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A statistical privacy mechanism is employed to generate data $U$ based on $(X,Y)$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. To this end, we use extended versions of the Functional Representation Lemma and Strong Functional Representation Lemma and combine them with a simple observation which we call separation technique. New lower bounds on privacy-utility trade-off are derived and we show that they can improve the previous bounds. We study the obtained bounds in different scenarios and compare them with previous results.

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arXiv2023

Private Variable-Length Coding with Sequential Encoder

A multi-user private data compression problem is studied. A server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is connected to an encoder. The encoder is connected through an unsecured link to a user. We assume that each file $Y_i$ is arbitrarily correlated with a private attribute $X$, which is assumed to be accessible by the encoder. Moreover, an adversary is assumed to have access to the link. The users and the encoder have access to a shared secret key $W$. We assume that at each time the user asks for a file $Y_{d_i}$, where $(d_1,\ldots,d_K)$ corresponds to the demand vector. The goal is to design the delivered message $\mathcal {C}=(\mathcal {C}_1,\ldots,\mathcal {C}_K)$ after the user send his demands to the encoder such that the average length of $\mathcal{C}$ is minimized, while satisfying: i. The message $\cal C$ does not reveal any information about $X$, i.e., $X$ and $\mathcal{C}$ are independent, which corresponds to the perfect privacy constraint; ii. The user is able to decode its demands, $Y_{d_i}$, by using $\cal C$, and the shared key $W$. Here, the encoder sequentially encode each demand $Y_{d_i}$ at time $i$, using the shared key and previous encoded messages. We propose a variable-length coding scheme that uses privacy-aware compression techniques. We study proposed upper and lower bounds on the average length of $\mathcal{C}$ in an example. Finally, we study an application considering cache-aided networks.

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arXiv2023

Bounds for Privacy-Utility Trade-off with Non-zero Leakage

The design of privacy mechanisms for two scenarios is studied where the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A privacy mechanism is employed to generate data $U$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. In the second scenario, the agent has additionally access to the private data. To this end, the Functional Representation Lemma and Strong Functional Representation Lemma are extended relaxing the independence condition and thereby allowing a certain leakage. Lower bounds on privacy-utility trade-off are derived for the second scenario as well as upper bounds for both scenarios. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds.

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arXiv2022

On the Privacy-Utility Trade-off With and Without Direct Access to the Private Data

We study an information theoretic privacy mechanism design problem for two scenarios where the private data is either observable or hidden. In each scenario, we first consider bounded mutual information as privacy leakage criterion, then we use two different per-letter privacy constraints. In the first scenario, an agent observes useful data $Y$ that is correlated with private data $X$, and wishes to disclose the useful information to a user. A privacy mechanism is designed to generate disclosed data $U$ which maximizes the revealed information about $Y$ while satisfying a bounded privacy leakage constraint. In the second scenario, the agent has additionally access to the private data. To this end, we first extend the Functional Representation Lemma and Strong Functional Representation Lemma by relaxing the independence condition and thereby allowing a certain leakage to find lower bounds for the second scenario with different privacy leakage constraints. Furthermore, upper and lower bounds are derived in the first scenario considering different privacy constraints. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds. Moreover, considering bounded mutual information as privacy constraint we show that if the common information and mutual information between $X$ and $Y$ are equal, then the attained upper bound in the second scenario is tight. Finally, the privacy-utility trade-off with prioritized private data is studied where part of $X$, i.e., $X_1$, is more private than the remaining part, i.e., $X_2$, and we provide lower and upper bounds.

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arXiv2022

Multi-User Privacy Mechanism Design with Non-zero Leakage

A privacy mechanism design problem is studied through the lens of information theory. In this work, an agent observes useful data $Y=(Y_1,...,Y_N)$ that is correlated with private data $X=(X_1,...,X_N)$ which is assumed to be also accessible by the agent. Here, we consider $K$ users where user $i$ demands a sub-vector of $Y$, denoted by $C_{i}$. The agent wishes to disclose $C_{i}$ to user $i$. Since $C_{i}$ is correlated with $X$ it can not be disclosed directly. A privacy mechanism is designed to generate disclosed data $U$ which maximizes a linear combinations of the users utilities while satisfying a bounded privacy constraint in terms of mutual information. In a similar work it has been assumed that $X_i$ is a deterministic function of $Y_i$, however in this work we let $X_i$ and $Y_i$ be arbitrarily correlated. First, an upper bound on the privacy-utility trade-off is obtained by using a specific transformation, Functional Representation Lemma and Strong Functional Representaion Lemma, then we show that the upper bound can be decomposed into $N$ parallel problems. Next, lower bounds on privacy-utility trade-off are derived using Functional Representation Lemma and Strong Functional Representaion Lemma. The upper bound is tight within a constant and the lower bounds assert that the disclosed data is independent of all $\{X_j\}_{i=1}^N$ except one which we allocate the maximum allowed leakage to it. Finally, the obtained bounds are studied in special cases.

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arXiv2022

Bounds for Privacy-Utility Trade-off with Per-letter Privacy Constraints and Non-zero Leakage

An information theoretic privacy mechanism design problem for two scenarios is studied where the private data is either hidden or observable. In each scenario, privacy leakage constraints are considered using two different measures. In these scenarios the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$ that is correlated with private data $X$, and wishes to disclose the useful information to a user. A privacy mechanism is designed to generate disclosed data $U$ which maximizes the revealed information about $Y$ while satisfying a per-letter privacy constraint. In the second scenario, the agent has additionally access to the private data. First, the Functional Representation Lemma and Strong Functional Representation Lemma are extended by relaxing the independence condition to find a lower bound considering the second scenario. Next, lower bounds as well as upper bounds on privacy-utility trade-off are derived for both scenarios. In particular, for the case where $X$ is deterministic function of $Y$, we show that our upper and lower bounds are asymptotically optimal considering the first scenario.

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arXiv2021

Data Disclosure with Non-zero Leakage and Non-invertible Leakage Matrix

We study a statistical signal processing privacy problem, 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 employs a privacy mechanism to generate data $U$ that can be released. We study the privacy mechanism design that maximizes the revealed information about $Y$ while satisfying a strong $\ell_1$-privacy criterion. When a sufficiently small leakage is allowed, we show that the optimizer vectors of the privacy mechanism design problem have a specific geometry, i.e., they are perturbations of fixed vector distributions. This geometrical structure allows us to use a local approximation of the conditional entropy. By using this approximation the original optimization problem can be reduced to a linear program so that an approximate solution for privacy mechanism can be easily obtained. The main contribution of this work is to consider non-zero leakage with a non-invertible leakage matrix. In an example inspired by water mark application, we first investigate the accuracy of the approximation. Then, we employ different measures for utility and privacy leakage to compare the privacy-utility trade-off using our approach with other methods. In particular, it has been shown that by allowing small leakage, significant utility can be achieved using our method compared to the case where no leakage is allowed.

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arXiv2021

A Design Framework for Strongly $χ^2$-Private Data Disclosure

In this paper, we study a stochastic disclosure control problem using information-theoretic methods. The useful data to be disclosed depend on private data that should be protected. Thus, we design a privacy mechanism to produce new data which maximizes the disclosed information about the useful data under a strong $χ^2$-privacy criterion. For sufficiently small leakage, the privacy mechanism design problem can be geometrically studied in the space of probability distributions by a local approximation of the mutual information. By using methods from Euclidean information geometry, the original highly challenging optimization problem can be reduced to a problem of finding the principal right-singular vector of a matrix, which characterizes the optimal privacy mechanism. In two extensions we first consider a scenario where an adversary receives a noisy version of the user's message and then we look for a mechanism which finds $U$ based on observing $X$, maximizing the mutual information between $U$ and $Y$ while satisfying the privacy criterion on $U$ and $Z$ under the Markov chain $(Z,Y)-X-U$.

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