Perspective Reformulations of the CTA Problem with L₂ Distances

Abstract

Any institution that disseminates data in aggregated form has the duty to ensure that individual confidential information is not disclosed, either by not releasing data or by perturbing the released data, while maintaining data utility. Controlled tabular adjustment (CTA) is a promising technique of the second type where a protected table that is close to the original one in some chosen distance is constructed. We attempt, for the first time, to solve CTA with Euclidean distances; this gives rise to difficult Mixed Integer Quadratic Problems (MIQPs) with pairs of linked semi-continuous variables. We provide a novel analysis of Perspective Reformulations (PRs) for this special structure; in particular, we devise a Projected PR (P 2 R) which is piecewise-conic but simplifies to a (nonseparable) MIQP when the instance is symmetric. We then compare different formulations of the CTA problem, showing that the ones based on P 2 R most often obtain better computational results.

Symmetric vs Asymmetric Protection Levels in SDC Methods for Tabular Data

“…Two symmetric tables exceeded the one hour time limit for CSP, so the final gap reached (in brackets) is notably higher than the required one. From Table 2, CTA is clearly more efficient for asymmetric than for symmetric instances; this is consistent with the results of [9], albeit they were for a quadratic version of CTA (i.e., using the 2 Euclidean instead of the 1 distance in the objective function). For CSP the pattern is not so definitive: asymmetric instances 4, 5 and, specially, 6 were slower than the corresponding symmetric variants.…”

“…A priori, asymmetric intervals could benefit the solution of mixed integer linear optimization problems, such as CTA and CSP. Indeed, some results along these lines were obtained in [9] for CTA with quadratic objectives. Another objective of this work is to check if such behaviour is observed for CTA and CSP in the solution of a set of hierarchical tables.…”

“…CTA replaces sensitive values by safe values (i.e., outside the safety interval), thus forcing changes in other cells to preserve the table additivity. CTA is also formulated as a mixed integer linear optimization problem, which can be solved optimally by general purpose solvers [9], or heuristically [13,2]. This work provides a formulation of CSP, CTA and IP from the same set of parameters.…”

A linear optimization-based method for data privacy in statistical tabular data

“…Among the recent literature on CTA variants we find [9,18]. Although CTA is not as widely used as cell suppression, it has been applied as one of the steps of other wider protection schemes, such as the pre-tabular protection method of [16].…”

Fix-and-relax approaches for controlled tabular adjustment

“…This CTA software is included in the tauArgus package [25] (http://neon.vb.cbs.nl/casc/tau.htm), used for many European national statistical institutes for the protection of tabular data. Among the recent literature on CTA variants we find [8,24]. In recent specialized workshops on statistical disclosure control, some NSAs stated that perturbative methods, like CTA, are gaining acceptance [31], and perturbative approaches are being used for the protection of national census tables (e.g., [21] for Germany).…”