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A Second Order Cone Formulation of Continuous CTA Model

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Privacy in Statistical Databases (PSD 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9867))

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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 \(\ell _1\) 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.

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Acknowledgments

The first author would like to thank Erling Andersen and Florian Jarre for the constructive discussion regarding the SOC model and Iryna Petrenko for her help in performing the calculations described in Sect. 5.

The authors would like to express their appreciation to Donald Malec for his careful reading of the paper and many useful suggestions.

Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors only and do not necessarily reflect the views of the Centers for Disease Control and Prevention.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Georgia Southern University, P.O. Box 8093, Statesboro, GA, 30460-8093, USA

    Goran Lesaja & Anna Oganian

  2. Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Jordi Girona 1–3, 08034, Barcelona, Catalonia, Spain

    Jordi Castro

  3. National Center for Health Statistics, 3311 Toledo Road, Hyatsville, MD, 20782, USA

    Anna Oganian

Authors
  1. Goran Lesaja
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  2. Jordi Castro
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  3. Anna Oganian
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Corresponding author

Correspondence to Goran Lesaja .

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Editors and Affiliations

  1. Universitat Rovira i Virgili, Tarragona, Spain

    Josep Domingo-Ferrer

  2. University of Zagreb, Zagreb, Croatia

    Mirjana Pejić-Bach

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Lesaja, G., Castro, J., Oganian, A. (2016). A Second Order Cone Formulation of Continuous CTA Model. In: Domingo-Ferrer, J., Pejić-Bach, M. (eds) Privacy in Statistical Databases. PSD 2016. Lecture Notes in Computer Science(), vol 9867. Springer, Cham. https://doi.org/10.1007/978-3-319-45381-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-45381-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45380-4

  • Online ISBN: 978-3-319-45381-1

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