Solving L1-CTA in 3D tables by an interior-point method for primal block-angular problems

The purpose of the field of statistical disclosure control is to avoid that confidential information could be derived from statistical data released by, mainly, national statistical agencies. Controlled tabular adjustment (CTA) is an emerging technique for the protection of statistical tabular data....

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Published in:TOP Vol. 21; no. 1; pp. 25 - 47
Main Authors: Castro, Jordi, Cuesta, Jordi
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2013
Springer
Subjects:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
Preconditioned conjugate gradient
Controlled tabular adjustment
Large-scale computational optimization
90C51
90C06
Statistical tabular data protection
90C90
Interior-point methods
Primal block-angular problems
Regularizations
90C08
ISSN:1134-5764, 1863-8279
Online Access:Get full text
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Abstract The purpose of the field of statistical disclosure control is to avoid that confidential information could be derived from statistical data released by, mainly, national statistical agencies. Controlled tabular adjustment (CTA) is an emerging technique for the protection of statistical tabular data. Given a table with sensitive information, CTA looks for the closest safe table. In this work we focus on CTA for three-dimensional tables using the L 1 norm for the distance between the original and protected tables. Three L 1 -CTA models are presented, giving rise to six different primal block-angular structures of the constraint matrices. The resulting linear programming problems are solved by a specialized interior-point algorithm for this constraints structure which solves the normal equations by a combination of Cholesky factorization and preconditioned conjugate gradients (PCG). In the past this algorithm was shown to be one of the most efficient approaches for some classes of block-angular problems. The effect of quadratic regularizations is also analyzed, showing that for three of the six primal block-angular structures the performance of PCG is guaranteed to improve. Computational results are reported for a set of large instances, which provide linear optimization problems of up to 50 million variables and 25 million constraints. The specialized interior-point algorithm is compared with the state-of-the-art barrier solver of the CPLEX 12.1 package, showing to be a more efficient choice for very large L 1 -CTA instances.
AbstractList The purpose of the field of statistical disclosure control is to avoid that confidential information could be derived from statistical data released by, mainly, national statistical agencies. Controlled tabular adjustment (CTA) is an emerging technique for the protection of statistical tabular data. Given a table with sensitive information, CTA looks for the closest safe table. In this work we focus on CTA for three-dimensional tables using the L 1 norm for the distance between the original and protected tables. Three L 1 -CTA models are presented, giving rise to six different primal block-angular structures of the constraint matrices. The resulting linear programming problems are solved by a specialized interior-point algorithm for this constraints structure which solves the normal equations by a combination of Cholesky factorization and preconditioned conjugate gradients (PCG). In the past this algorithm was shown to be one of the most efficient approaches for some classes of block-angular problems. The effect of quadratic regularizations is also analyzed, showing that for three of the six primal block-angular structures the performance of PCG is guaranteed to improve. Computational results are reported for a set of large instances, which provide linear optimization problems of up to 50 million variables and 25 million constraints. The specialized interior-point algorithm is compared with the state-of-the-art barrier solver of the CPLEX 12.1 package, showing to be a more efficient choice for very large L 1 -CTA instances.
Author Castro, Jordi
Cuesta, Jordi
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  surname: Cuesta
  fullname: Cuesta, Jordi
  organization: Statistics and Operations Research unit, Dept. of Chemical Engineering, Universitat Rovira i Virgili
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Cites_doi 10.1137/0802028
10.1007/s10107-003-0379-5
10.1016/j.ejor.2004.08.034
10.1080/10556789808805699
10.1007/BF00249643
10.1287/ijoc.1060.0185
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Issue 1
Keywords Preconditioned conjugate gradient
Controlled tabular adjustment
Large-scale computational optimization
90C51
90C06
Statistical tabular data protection
90C90
Interior-point methods
Primal block-angular problems
Regularizations
90C08
Language English
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Castro (CR4) 2007; 36
Castro, Cuesta (CR6) 2011; 130
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SubjectTerms Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
Title Solving L1-CTA in 3D tables by an interior-point method for primal block-angular problems
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