# Questions tagged [differential-privacy]

Differential privacy aims to provide means to maximize the accuracy of queries from statistical databases while minimizing the chances of identifying its records.

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### Explaining the reason of radically more accuracy while using different set of hash functions instead of same set of hash functions on some operations

So I am looking for an explanation of an experiment. In this experiment, I took a set of k hash functions. Say the total number of data points I am working on is d. Call an algorithm A which used that ...
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### Laplace Inequality

I am trying to prove that if $r_i \sim Lap(0,1/\varepsilon)$ where $\varepsilon >0$ then: $$Pr[r_i \geq 1+r^*] \geq e^{-\varepsilon}Pr[r_i \geq r^{*}]$$. I know that for $r*>0$ it satisfies ...
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### The sensitivity in differential privacy with deep learning

In differentially private deep learning, the sensitivity is determined by clipping gradient norm(Abadi's paper). In this paper, when the clipping gradient norm is C, the sensitivity is C. Why the ...
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### $(\epsilon, \delta)$-differential privacy: main motivation of $\delta$

I am wondering why (not how) we relax $\epsilon$-differential privacy to $(\epsilon, \delta)$-differential privacy. Is the main motivation to reduce the variance of the noise added to the query with a ...
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I have a problem understanding the proof of the corollary of Advanced Composition Theorem Advanced Composition: For all $\varepsilon,\delta,\delta' \geq 0$ the class of $('\varepsilon,\delta)$-...
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### Interpretation of advanced composition theorem of differential privacy

In "The Algorithmic Foundations of Differential Privacy" book, Advanced Decomposition Theorem (Thm 3.20) is stated as follows: For all "$\epsilon, \delta, \delta' \geq 0$, the class of ...
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### Differential Privacy of the Laplace mechanism with non-deterministic function

This question is about the proof of the differential privacy of the laplace mechanism. All more detailled explanations I found of the proof, that the laplace mechanism is $\epsilon$-differentially ...
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### Proof of the basic differential privacy composition theorem

The basic composition theorem in differential privacy states, that if I have mechanisms $M_1$, which is $(\epsilon_1, \delta_1)$-differential private, and $M_2$, which is $(\epsilon_2, \delta_2)$-...
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### questions about sensitivity in differential privacy

Ted here (What does the term "differential" in "differential privacy" mean?) describes the difference between local and global sensitivity as "By contrast, local and global ...
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### Laplace mechanism in Differential Privacy

From The Algorithmic Foundations of Diļ¬erential Privacy It wrote that : But from this pdf I am confused which one is right, or I misunderstand. In second method, after I compute Pr[v], and then ...
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### Confusing notation in the definition of differential privacy

I've started looking into differential privacy from scratch following "The Algorithmic Foundations of Differential Privacy" by Dwork and Roth (freely available online). The mathematical notation is ...
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### Differential privacy basics: Universe \mathcal{X} and database $x$

The "Algorithmic Foundations of Differential Privacy" book (DOI: 10.1561/0400000042) introduces formally the "universe" and "database" on page 17 roughly as: $\mathcal{X}$ is a universe databases $x$ ...
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### Sensitivity of probability measure in differential privacy

I know that we need some sort of sensitivity(global, local) to calculate noise that needs to be added for differential privacy. The noise is the maximum difference between two neighboring datasets. ...
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### Differential Privacy: why $\delta$ negligible on the row numbers?

The definition of differential privacy says that an algorithm $M$ is $(\epsilon,\delta)$-differentially private if $$P(M(x \in D) \in S)\leq e^\epsilon P(M(x \in D')\in S) + \delta$$ where $D,D'$ ...
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### Norms in differential privacy

I know that perturbation should be proportional to the $\text{L}_1$-sensitivity of the function if someone wants ($\epsilon,0$)-differential privacy, and proportional to the $\text{L}_2$-sensitivity ...
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### What does the term “differential” in “differential privacy” mean?

I'm new in Differential Privacy (DP) and I have two questions: Why do we have the term differential in differential privacy? Are The local and global differential privacy and global and local ...
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### what is the relationship between epsilon and sensitivity in the Differential-Privacy?

In some Differential-Privacy(DP) papers, they use epsilon as the x-axis in the figures of the experiments' result while other papers use the sensitivity. What is the relationship between epsilon and ...
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### Why does Gausian use less noise than Laplace

Why does Gaussian noise apply less noise than Laplace? has to do maybe that Laplace is been used with queries and each query may have different sensitivity? or maybe because Gaussian is been used on ...
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### privacy enhancing techniques on image data

To give some context: I am looking for a suite of techniques and tools that can theoretically enable me to conduct analysis such as classification on image datasets in a manner in which a naive ...
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### Differential privacy on medical data

When we apply the differential privacy on medical data to protect the personal data of the patients, how the doctors can access the original data to analyze them and to intervene in real-time. In ...
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### Are there any differences between PIR, oblivious transfer and differential privacy?

I am trying to make a taxonomy of the different purposes of some cryptographic protocols. Generally speaking, the purpose of PIR, oblivious transfer and differential privacy--it sounds as if they were ...
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### Mechanisms for Locally Private data release for continuous data

Most of the Local Differential Privacy mechanisms I've seen in the literature operate on discrete data, e.g. Randomized Response or RAPPOR. Can you point me to some LDP mechanisms for continuous data (...
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### Why the definition in $\epsilon$-differential privacy is multiplicative rather than additiveļ¼

According to its mathematical definition, a random algorithm $M: D\rightarrow R$ satisfies $\epsilon$-differential privacy if the adjacent datasets $x, y \in D$ where $D$ is a whole dataset and ...
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### Differential privacy definition

Differential privacy defines "privacy" of a mechanism $A$ as the "closeness" of the two distribution $Pr[A(D) \in S]$ and $Pr[A(D') \in S]$ where $D,D'$ differ in one element. And the distance between ...
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### Differential Privacy and appropriate noise distribution

In differential privacy solutions and more specifically for queries that they do entail counting the proposed solutions define the Laplace distribution that is best calibrated for low error. Other ...
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### Differential privacy on multiple queries ā what is the behavior?

Differential privacy framework still continue to be obscure in the following case: If I make a set of queries, I can join their output to restore the original data. For this issue we have composition ...
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### Intuitive explanation of the $\varepsilon$ parameter in differential privacy

I think I have a decent intuitive understanding of what the $\delta$ parameter means in $(\varepsilon,\delta)$-differential privacy: I can explain it to a non-specialist in terms of "what are the ...
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### Differential privacy and Shamir's scheme

I have been unable to find any proofs (for my own reference) that demonstrate that Shamir's secret sharing scheme does (or does not) satisfy the definition of $\textbf{differential privacy}$ as ...
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### Laplace Mechanism Proof: Why this product operator?

The equation below shows the proof of Laplace mechanism for differential privacy. I am not understanding the product operator, is this a common rule?  \frac{p_x(z)}{p_y(z)} = \prod_{i=1}^{k}\left(\...
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