Locally differentially-private distribution estimation

A number of studies have recently been made on discrete distribution estimation in the local model, in which users obfuscate their personal data (e.g., location, response in a survey) by themselves and a data collector estimates a distribution of the original personal data from the obfuscated data. Unlike the centralized model, in which a trusted database administrator can access all users’ personal data, the local model does not suffer from the risk of data leakage. A representative privacy metric in this model is LDP (Local Differential Privacy), which controls the amount of information leakage by a parameter ∈ called privacy budget. When ∈ is small, a large amount of noise is added to the personal data, and therefore users’ privacy is strongly protected. However, when the number of users ℕ is small (e.g., a small-scale enterprise may not be able to collect large samples) or when most users adopt a small value of ∈, the estimation of the distribution becomes a very challenging task. The goal of this paper is to accurately estimate the distribution in the cases explained above. To achieve this goal, we focus on the EM (Expectation-Maximization) reconstruction method, which is a state-of-the-art statistical inference method, and propose a method to correct its estimation error (i.e., difference between the estimate and the true value) using the theory of Rilstone et al. We prove that the proposed method reduces the MSE (Mean Square Error) under some assumptions.We also evaluate the proposed method using three largescale datasets, two of which contain location data while the other contains census data. The results show that the proposed method significantly outperforms the EM reconstruction method in all of the datasets when ℕ or ∈ is small.

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“…We can show that E[d T c 2 ] is 0 in the same way. E[d T c 2 ] can be written, using (37) and (45), as follows:…”

Section: A Proof Of Propositionmentioning

confidence: 99%

“…A number of studies have recently been made on LPDE (e.g., [3,17,25,30,31,37,40,44]), mainly from the perspective of privacy metrics, obfuscation mechanisms, and statistical inference methods. A representative privacy metric in the local model is LDP (Local Differential Privacy) [11].…”

Section: Introductionmentioning

confidence: 99%

Toward Distribution Estimation under Local Differential Privacy with Small Samples

Murakami

Hino

Sakuma

2018

Proceedings on Privacy Enhancing Technologies

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“…Critical densities ρ C as functions of the transferred momentum q, in symmetric nuclear matter and for the case of two Skyrme functionals that either do not include or include tensor terms [50]. They are displayed for different channels, and the saturation density is highlighted with a horizontal line.…”

Section: Instabilitiesmentioning

confidence: 99%

Covariance analysis for energy density functionals and instabilities

Roca-Maza¹,

Paar²

2015

J. Phys. G: Nucl. Part. Phys.

140

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We present the covariance analysis of two successful nuclear energy density functionals, (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear energy density functional based on density dependent meson-nucleon couplings. The covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors. We show, for our selected test nucleus 208 Pb, that when the constraint on a property A included in the fit is relaxed, correlations with other observables B become larger; on the other hand, when a strong constraint is imposed on A, the correlations with other properties become very small. We also provide a brief review, partly connected with the covariance analysis, of some instabilities displayed by several energy density functionals currently used in nuclear physics.

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“…This is already established for the analogous (isoscalar) Λ-Λ hyperon interaction, where the scattering length is an order of magnitude weaker than the corresponding N-N. Recent calculations of the range of the d * − d * interaction [16] ‡ also indicate an interaction of smaller magnitude and shorter range. We take a ′ v over all values from 0 up to the NN limit of 30 MeV to to explore the sensitivity of the condensate properties to the detailed nature of the d * (2380) interaction.…”

Section: Estimates Of D * (2380)-bec Stabilitymentioning

confidence: 67%

“…This results in a force showing suppression of longer range interactions and strong short range attraction with even stronger shorter range repulsion. The detailed calculations will be published in a forthcoming paper [16]. The results provide an indicative parameter space for a bound d * (2380)-BEC, defining regions where the energy required to form the d * (2380) from nucleons is exceeded by the binding energy available in forming the d * (2380)-BEC.…”

Section: Estimates Of D * (2380)-bec Stabilitymentioning

confidence: 99%

A new possibility for light-quark dark matter

Bashkanov¹,

Watts²

2020

J. Phys. G: Nucl. Part. Phys.

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Despite many decades of study the physical origin of "dark matter" in the Universe remains elusive. In this letter we calculate the properties of a completely new dark matter candidate -Bose-Einstein condensates formed from a recently discovered bosonic particle in the light-quark sector, the d * (2380) hexaquark. In this first study, we show stable d * (2380) Bose-Einstein condensates could form in the primordial early universe, with a production rate sufficiently large that they are a plausible new candidate for dark matter. Some possible astronomical signatures of such dark matter are also presented.

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Locally differentially-private distribution estimation

Cited by 22 publications

References 9 publications

Toward Distribution Estimation under Local Differential Privacy with Small Samples

Toward Distribution Estimation under Local Differential Privacy with Small Samples

Covariance analysis for energy density functionals and instabilities

A new possibility for light-quark dark matter

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