Estimation of Regression Parameters from Noise Multiplied Data

Lin, Yan-Xia; Wise, Phillip

doi:10.29012/jpc.v4i2.622

Cited by 6 publications

(11 citation statements)

References 20 publications

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“…The above criterion was also used by Klein et al (2014) to measure the level of privacy protection in the context of noise multiplication to protect extreme values, and it is similar to a criterion used by Lin and Wise (2012). Notice that if the probability (23) is small, then we would conclude that there is a high level of protection against disclosure; and if this probability is large, then we would conclude that there is a low level of protection against disclosure.…”

Section: Disclosure Risk Evaluation Of Singly Versus Multiply Imputedmentioning

confidence: 99%

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

Kampel

Sinha

2015

JPC

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In this paper we develop likelihood-based finite sample inference based on singly imputed partially synthetic data, when the original data follow either a multivariate normal or a multiple linear regression model. We assume that the synthetic data are generated by using the plug-in sampling method, where unknown parameters in the data model are set equal to observed values of their point estimators based on the original data, and synthetic data are drawn from this estimated version of the model. Empirical studies are presented to show that the proposed methods do indeed perform as the theory predicts, and to compare the proposed methods for singly imputed synthetic data with the combining rules that are used to analyze multiply imputed partially synthetic data. Some theoretical comparisons between singly and multiply imputed partially synthetic data inference are also provided. A data analysis example and disclosure risk evaluation of singly and multiply imputed partially synthetic data is presented based on public use data from the Current Population Survey. We discuss the specific conditions under which the proposed methodology will yield valid inference, and evaluate the performance of the methodology when certain conditions do not hold. We outline some ways to extend the proposed methodology for certain scenarios where the required set of conditions do not hold.

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Section: Disclosure Risk Evaluation Of Singly Versus Multiply Imputedmentioning

confidence: 99%

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

Kampel

Sinha

2015

JPC

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“…It is not necessary for the realization ofŶ 1 to be exactly equal to y 1 -the degree of accuracy required for disclosure must be determined by the statistical agency. The following definition of disclosure risk we adopt is similar to that used by Lin and Wise (2012) and Klein et al(2014).…”

Section: Defining Disclosurementioning

confidence: 99%

A New Algorithm for Protecting Aggregate Business Microdata via a Remote System

Lin

Chipperfield

et al. 2016

Privacy in Statistical Databases

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Releasing business microdata is a challenging problem for many statistical agencies. Businesses with distinct continuous characteristics such as extremely high income could easily be identified while these businesses are normally included in surveys representing the population. In order to provide data users with useful statistics while maintaining confidentiality, some statistical agencies have developed online based tools to allow users to specify and request tables created from microdata. These tools only release perturbed cell values generated from automatic output perturbation algorithms in order to protect each underlying observation against various attacks, such as differencing attacks. An example of the perturbation algorithms has been proposed by Thompson et al. (2013). The algorithm focuses largely on reducing disclosure risks without addressing much on data utility. As a result, the algorithm has limitations, including a limited scope of applicable cells and uncontrolled utility loss. In this paper we introduce a new algorithm for generating perturbed cell values. As a comparison, The new algorithm allows more control over utility loss, while it could also achieve better utility-disclosure tradeoffs in many cases, and is conjectured to be applicable to a wider scope of cells. Abstract. Releasing business microdata is a challenging problem for many statistical agencies. Businesses with distinct continuous characteristics such as extremely high income could easily be identified while these businesses are normally included in surveys representing the population. In order to provide data users with useful statistics while maintaining confidentiality , some statistical agencies have developed online based tools to allow users to specify and request tables created from microdata. These tools only release perturbed cell values generated from automatic output perturbation algorithms in order to protect each underlying observation against various attacks, such as differencing attacks. An example of the perturbation algorithms has been proposed by Thompson et al. (2013). The algorithm focuses largely on reducing disclosure risks without addressing much on data utility. As a result, the algorithm has limitations, including a limited scope of applicable cells and uncontrolled utility loss. In this paper we introduce a new algorithm for generating perturbed cell values. As a comparison, The new algorithm allows more control over utility loss, while it could also achieve better utility-disclosure tradeoffs in many cases, and is conjectured to be applicable to a wider scope of cells.

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“…We assume thatŷ i is some function of the data that are released after a method of statistical disclosure control has been applied to the y i values that exceed C. We measure the level of privacy protection using the following criterion, which is similar to the one used by Lin and Wise [21]:…”

Section: Disclosure Risk Evaluationmentioning

confidence: 99%

“…To address the issue of disclosure risk, we present an evaluation in the context of a real data example (Section 5.2). Our methodology for evaluating disclosure risk is based on a criterion similar to one used by Lin and Wise [21] for the same purpose. We also evaluate the disclosure risk of synthetic data based on this same criterion, and make some comparisons with perturbation under noise multiplication.…”

Section: Introductionmentioning

confidence: 99%

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Noise Multiplication for Statistical Disclosure Control of Extreme Values in Log-normal Regression Samples

Kampel

Mathew

Sinha

2014

JPC

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In this article multiplication of original data values by random noise is suggested as a disclosure control strategy when only the top part of the data is sensitive, as is often the case with income data. The proposed method can serve as an alternative to top coding which is a standard method in this context. Because the log-normal distribution usually fits income data well, the present investigation focuses exclusively on the log-normal. It is assumed that the log-scale mean of the sensitive variable is described by a linear regression on a set of non-sensitive covariates, and we show how a data user can draw valid inference on the parameters of the regression. An appealing feature of noise multiplication is the presence of an explicit tuning mechanism, namely, the noise generating distribution. By appropriately choosing this distribution, one can control the accuracy of inferences and the level of disclosure protection desired in the released data. Usually, more information is retained on the top part of the data under noise multiplication than under top coding. Likelihood based analysis is developed when only the large values in the data set are noise multiplied, under the assumption that the original data form a sample from a log-normal distribution. In this scenario, data analysis methods are developed under two types of data releases: (I) each released value includes an indicator of whether or not it has been noise multiplied, and (II) no such indicator is provided. A simulation study is carried out to assess the accuracy of inference for some parameters of interest. Since top coding and synthetic data methods are already available as disclosure control strategies for extreme values, some comparisons with the proposed method are made through a simulation study. The results are illustrated with a data analysis example based on 2000 U.S. Current Population Survey data. Furthermore, a disclosure risk evaluation of the proposed methodology is presented in the context of the Current Population Survey data example, and the disclosure risk of the proposed noise multiplication method is compared with the disclosure risk of synthetic data.

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Estimation of Regression Parameters from Noise Multiplied Data

Cited by 6 publications

References 20 publications

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

A New Algorithm for Protecting Aggregate Business Microdata via a Remote System

Noise Multiplication for Statistical Disclosure Control of Extreme Values in Log-normal Regression Samples

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