Home > Research > Publications & Outputs > An Information Theoretic approach to Post Rando...

Electronic data

  • S_C_MAIN_FILE

    Accepted author manuscript, 7.32 MB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

Links

Text available via DOI:

View graph of relations

An Information Theoretic approach to Post Randomization Methods under Differential Privacy

Research output: Contribution to journalJournal articlepeer-review

Published
Close
<mark>Journal publication date</mark>1/09/2020
<mark>Journal</mark>Statistics and Computing
Volume30
Number of pages15
Pages (from-to)1347–1361
Publication StatusPublished
Early online date1/06/20
<mark>Original language</mark>English

Abstract

Post Randomization Methods (PRAM) are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix M and a specified variable, an individual belonging to category i is changed to category j with probability Mi,j . Every approach to choose the randomization matrix M has to balance between two desiderata: 1) preserving as much statistical information from the raw data as possible; 2) guaranteeing the privacy of individuals in the dataset.
This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose M as the solution of a constrained maximization problems. Specifically, M is chosen as the solution of a constrained maximization problem, where we maximize the Mutual Information between raw and transformed data,
given the constraint that the transformation satisfies the notion of Differential Privacy. For the general Categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms.