p-probabilistic k-anonymous microaggregation for the anonymization of surveys with uncertain participation

We develop a probabilistic variant of k-anonymous microaggregation which we term p-probabilistic resorting to a statistical model of respondent participation in order to aggregate quasi-identifiers in such a manner that k-anonymity is concordantly enforced with a parametric probabilistic guarantee. Succinctly owing the possibility that some respondents may not finally participate, sufficiently larger cells are created striving to satisfy k-anonymity with probability at least p. The microaggregation function is designed before the respondents submit their confidential data. More precisely, a specification of the function is sent to them which they may verify and apply to their quasi-identifying demographic variables prior to submitting the microaggregated data along with the confidential attributes to an authorized repository. We propose a number of metrics to assess the performance of our probabilistic approach in terms of anonymity and distortion which we proceed to investigate theoretically in depth and empirically with synthetic and standardized data. We stress that in addition to constituting a functional extension of traditional microaggregation, thereby broadening its applicability to the anonymization of statistical databases in a wide variety of contexts, the relaxation of trust assumptions is arguably expected to have a considerable impact on user acceptance and ultimately on data utility through mere availability.Peer ReviewedPostprint (author's final draft

The Effect of Microaggregation Procedures on the Estimation of Linear Models: A Simulation Study

Microaggregation is a set of procedures that distort empirical data in order to guarantee the factual anonymity of the data. At the same time the information content of data sets should not be reduced too much and should still be useful for scientific research. This paper investigates the effect of microaggregation on the estimation of a linear regression by ordinary least squares. It studies, by way of an extensive simulation experiment, the bias of the slope parameter estimator induced by various microaggregation techniques. Some microaggregation procedures lead to consistent estimates while others imply an asymptotic bias for the estimator

Estimation of a Linear Regression under Microaggregation with the Response Variable as a Sorting Variable

Microaggregation is one of the most frequently applied statistical disclosure control techniques for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. However, while reducing the disclosure risk of data files, the technique also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a linear model in continuous variables. We show that parameter estimates are biased if the dependent variable is used to form the groups. Using this result, we develop a consistent estimator that removes the aggregation bias. Moreover, we derive the asymptotic covariance matrix of the corrected least squares estimator

The Effect of Single-Axis Sorting on the Estimation of a Linear Regression

Microaggregation is one of the most important statistical disclosure control techniques for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. In this paper, we consider single-axis sorting, a frequently applied microaggregation technique where the formation of groups depends on the magnitude of a sorting variable related to the variables in the data set. The paper deals with the impact of this technique on a linear model in continuous variables. We show that parameter estimates are asymptotically biased if the sorting variable depends on the response variable of the linear model. Using this result, we develop a consistent estimator that removes the aggregation bias. Moreover, we derive the asymptotic covariance matrix of the corrected least squares estimator

Statistical Inference in a Simple Linear Model Under Microaggregation

A problem statistical offices are increasingly faced with is guaranteeing confidentiality when releasing microdata sets. One method to provide safe microdata is to reduce the information content of a data set by means of masking procedures. A widely discussed masking procedure is microaggregation, a technique where observations are grouped and replaced with their corresponding group means. However, while reducing the disclosure risk of a data file, microaggregation also affects the results of statistical analyses. We focus on the effect of microaggregation on a simple linear model. In a previous paper we have shown how to correct for the aggregation bias of the naive least-squares estimator that occurs when the dependent variable is used to group the data. The present paper deals with the asymptotic variance of the corrected least-squares estimator and with the asymptotic variance of the naive least-squares estimator when either the dependent variable or the regressor is used to group the data. We derive asymptotic confidence intervals for the slope parameter. Furthermore, we show how to test for the significance of the slope parameter by analyzing the effect of microaggregation on the asymptotic power function of the naive t-test

Mathematically optimized, recursive prepartitioning strategies for k-anonymous microaggregation of large-scale datasets

© Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The technical contents of this work fall within the statistical disclosure control (SDC) field, which concerns the postprocessing of the demographic portion of the statistical results of surveys containing sensitive personal information, in order to effectively safeguard the anonymity of the participating respondents. A widely known technique to solve the problem of protecting the privacy of the respondents involved beyond the mere suppression of their identifiers is the k-anonymous microaggregation. Unfortunately, most microaggregation algorithms that produce competitively low levels of distortions exhibit a superlinear running time, typically scaling with the square of the number of records in the dataset. This work proposes and analyzes an optimized prepartitioning strategy to reduce significantly the running time for the k-anonymous microaggregation algorithm operating on large datasets, with mild loss in data utility with respect to that of MDAV, the underlying method. The optimization strategy is based on prepartitioning a dataset recursively until the desired k-anonymity parameter is achieved. Traditional microaggregation algorithms have quadratic computational complexity in the form T(n2). By using the proposed method and fixing the number of recurrent prepartitions we obtain subquadratic complexity in the form T(n3/2), T(n4/3), ..., depending on the number of prepartitions. Alternatively, fixing the ratio between the size of the microcell and the macrocell on each prepartition, quasilinear complexity in the form T(nlog¿n) is achieved. Our method is readily applicable to large-scale datasets with numerical demographic attributes.Peer ReviewedPostprint (author's final draft