A Second Order Cone Formulation of Continuous CTA Model

Document Type

Conference Proceeding

Publication Date

8-31-2016

Publication Title

Proceedings of PSD 2016: Privacy in Statistical Databases

DOI

10.1007/978-3-319-45381-1_4

ISBN

978-3-319-45381-1

Abstract

In this paper we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using ℓ1ℓ1 or ℓ2ℓ2 norm; with each measure having its advantages and disadvantages. Recently, in [4] a regularization of the ℓ1ℓ1-CTA using Pseudo-Huber function was introduced in an attempt to combine positive characteristics of both ℓ1ℓ1-CTA and ℓ2ℓ2-CTA. All three models can be solved using appropriate versions of Interior-Point Methods (IPM). It is known that IPM in general works better on well structured problems such as conic optimization problems, thus, reformulation of these CTA models as conic optimization problem may be advantageous. We present reformulation of Pseudo-Huber-CTA, and ℓ1ℓ1-CTA as Second-Order Cone (SOC) optimization problems and test the validity of the approach on the small example of two-dimensional tabular data set.

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