Recent advances in optimization techniques for statistical tabular data protection

Abstract

One of the main services of National Statistical Agencies (NSAs) for the current Information Society is the dissemination of large amounts of tabular data, which is obtained from microdata by crossing one or more categorical variables. NSAs must guarantee that no confidential individual information can be obtained from the released tabular data. Several statistical disclosure control methods are available for this purpose. These methods result in large linear, mixed integer linear, or quadratic mixed integer linear optimization problems. This paper reviews some of the existing approaches, with an emphasis on two of them: cell suppression problem (CSP) and controlled tabular adjustment (CTA). CSP and CTA have concentrated most of the recent research in the tabular data protection field. The particular focus of this work is on methods and results of practical interest for end-users (mostly, NSAs). Therefore, in addition to the resulting optimization models and solution approaches, computational results comparing the main optimization techniques-both optimal and heuristic-using real-world instances are also presented.

Perspective Reformulations of the CTA Problem with L2 Distances

“…since one seeks for the released values x that are closest (in the given norm) to the true values a, compatible with the relationships that a is known to have to satisfy, and protected according to (6). Of course, the disjunctive constraints (6) are the difficult part of the problem, their feasible region being nonconvex.…”

“…This justifies the interest in statistical disclosure control, i.e., the set of techniques that can be deployed to protect sensitive information. In particular, the focus of this work is on tabular data protection; seminal work on this field can be found in [2], and the current state-of-the-art is described in the recent surveys of [25] and [6], as well as in the monographs [27,22]. Although tabular data provide aggregated information, the publication of some cells may jeopardize individual information.…”

Fix-and-relax approaches for controlled tabular adjustment

“…For each cell, the table may report either the number of individuals (frequency tables) or information about another variable (magnitude tables). More details can be found in the recent survey [5] and the monographs [26,27]. Although cell tables report aggregated information for several respondents-so they could be considered anonymized-there is a risk of disclosing individual data.…”

“…These tables are obtained by crossing a particular categorical variable with a set of, say, h categorical variables that have a hierarchical relation; this results in a set of h two-dimensional tables with some common cells. For instance, Figure 2 (from [5]) illustrates a particular 1H2D table. The left subtable shows number of respondents for "region"×"profession"; the middle subtable is a "zoom in" of region R 2 , providing the number of respondents in municipalities of this region; finally the right subtable details the ZIP codes of municipality R 21 .…”

“…Several approaches have been tried to speed up the solution time. A straightforward Benders reformulation of the problem was attempted in [7], but promising results were only obtained for two-dimensional tables (i.e., tables obtained by crossing two categorical variables, whose constraints are represented by a node-arc network incidence matrix [5]). Heuristic and metaheuristic methods were attempted in [22], but they only solved small two-dimensional and three-dimensional tables of up to 625 and 8000 cells, respectively, while we consider in this work much more complex synthetic and real tables from the literature, of up to 200000 and 36000 cells, respectively.…”