A Second Order Cone Formulation of Continuous CTA Model

• Published in: Privacy in Statistical Databases Vol. 9867; pp. 41 - 53
• Main Authors: Lesaja, Goran, Castro, Jordi, Oganian, Anna
• Format: Book Chapter Journal Article Publication
• Language: English
• Published: Switzerland Springer International Publishing AG 2016; Springer International Publishing; Springer
• Series: Lecture Notes in Computer Science
• Subjects: 49 Calculus of variations and optimal control; optimization; Classificació AMS; Controlled tabular adjustment models; Convex optimization; Interior-Point Methods; Investigació operativa; Matemàtiques i estadística; Optimització; Pseudo-Huber Function; Public administration; Second-order cone optimization; Statistical disclosure limitation (control); Àrees temàtiques de la UPC; convex optimization; second-order cone optimization; pseudo-Huber function; controlled tabular adjustment models; interior-point methods; Statistical disclosure limitation (control)
• ISBN: 9783319453804; 3319453807
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-45381-1_4

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 $$\ell _1$$ or $$\ell _2$$ norm; with each measure having its advantages and disadvantages. Recently, in [4] a regularization of the $$\ell _1$$ -CTA using Pseudo-Huber function was introduced in an attempt to combine positive characteristics of both $$\ell _1$$ -CTA and $$\ell _2$$ -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 $$\ell _1$$ -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.