On the Discrepancy Measures for the Optimal Equal Probability Partitioning in Bayesian Multivariate Micro-Aggregation

摘要

Data holders, such as statistical institutions and financial organizations, have a very serious and demanding task when producing data for official and public use. It's about controlling the risk of identity disclosure and protecting sensitive information when they communicate data-sets among themselves, to governmental agencies and to the public. One of the techniques applied is that of micro-aggregation. In a Bayesian setting, micro-aggregation can be viewed as the optimal partitioning of the original data-set based on the minimization of an appropriate measure of discrepancy, or distance, between two posterior distributions, one of which is conditional on the original data-set and the other conditional on the aggregated data-set. Assuming d-variate normal data-sets and using several measures of discrepancy, it is shown that the asymptotically optimal equal probability m-partition of R-d, with m(1/d) is an element of N, is the convex one which is provided by hypercubes whose sides are formed by hyper-planes perpendicular to the canonical axes, no matter which discrepancy measure has been used. On the basis of the above result, a method that produces a sub-optimal partition with a very small computational cost is presented.