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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - An Information Theoretic approach to Post Randomization Methods under Differential Privacy
AU - Ayed, Fadhel
AU - Battiston, Marco
AU - Camerlenghi, Federico
PY - 2020/9/1
Y1 - 2020/9/1
N2 - 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.
AB - 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.
KW - Post Randomization Methods
KW - Disclosure risk
KW - Mutual Information
KW - Differential Privacy
KW - Categorical Variables
U2 - 10.1007/s11222-020-09949-3
DO - 10.1007/s11222-020-09949-3
M3 - Journal article
VL - 30
SP - 1347
EP - 1361
JO - Statistics and Computing
JF - Statistics and Computing
SN - 0960-3174
ER -