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A Second Order Cone Formulation of Continuous CTA Model
Goran Lesaja1, Jordi Castro2, Anna Oganian1,3
1Department of Mathematical Sciences, Georgia Southern University, P.O. Box 8093, Statesboro, GA 30460-8093, U.S.A.
Privacy in Statistical Databases. PSD (Conference : 2004- )
|November 21, 2019
Summary
This study introduces a new method for protecting sensitive tabular data using Controlled Tabular Adjustment (CTA) models. The research reformulates Pseudo-Huber-CTA and ℓ₁-CTA as Second-Order Cone optimization problems for improved data security.
Area of Science:
- Statistics
- Data Security
- Optimization
Background:
- Statistical disclosure limitation is crucial for protecting sensitive information in tabular data.
- Controlled Tabular Adjustment (CTA) models aim to find the closest "safe" table to original data.
- Existing CTA models (ℓ₁-CTA, ℓ₂-CTA) have distinct advantages and disadvantages.
Purpose of the Study:
- To reformulate Pseudo-Huber-CTA and ℓ₁-CTA models as Second-Order Cone (SOC) optimization problems.
- To explore the benefits of conic optimization for solving CTA models.
- To test the validity of the proposed reformulation on a small dataset.
Main Methods:
- Reformulation of Pseudo-Huber-CTA and ℓ₁-CTA as Second-Order Cone (SOC) optimization problems.
- Utilizing Interior-Point Methods (IPM) for solving the reformulated conic optimization problems.
- Testing the approach on a two-dimensional tabular data set.
Main Results:
- Demonstrated the successful reformulation of Pseudo-Huber-CTA and ℓ₁-CTA into SOC optimization problems.
- The reformulation potentially enhances the efficiency of solving these statistical disclosure limitation models.
- Initial tests on a small dataset validate the proposed approach.
Conclusions:
- Reformulating CTA models as SOC problems offers a promising avenue for statistical disclosure limitation.
- This approach may leverage the strengths of Interior-Point Methods for well-structured conic problems.
- Further research can explore the scalability and application of this method to larger datasets.
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