An information theoretic approach to post randomization methods under differential privacy
Fadhel Ayed, Marco Battiston, Federico Camerlenghi · Statistics and Computing · 2020
Abstract Post randomization methods are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrixMand a specified variable, an individual belonging to categoryiis changed to categoryjwith probability $$M_{i,j}$$ Mi,j . Every approach to choose the randomization matrixMhas 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 chooseMas the solution of a constrained maximization problems. Specifically,Mis 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.