A CTA Model Based on the Huber Function

Abstract

Minimum distance controlled tabular adjustment (CTA) is an emerging perturbative method of statistical disclosure control for tabular data. The goal of CTA is to find the closest safe table to some original tabular data with sensitive information. Closeness is usually measured by l1 or l2 distances. Distance l1 provides solutions with a smaller l0 norm than l2 (i.e., with a lesser number of changes with respect to the original table). However the optimization problem formulated with l2 requires half the number of variables than that for l1, and it is more efficiently solved. In this work a pseudo-Huber function (which is a continuous nonlinear approximation of the Huber function) is considered to measure the distance between the original and protected tables. This pseudo-Huber function approximates l1 but can be formulated with the same number of variables than l2. It results in a nonlinear convex optimization problem which, theoretically, can be solved in polynomial time. Some preliminary results using the Huber-CTA model are reported.