  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 $M_{i,j}$. 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.
