  Traditional perturbative statistical disclosure control (SDC) approaches such
as microaggregation, noise addition, rank swapping, etc, perturb the data in an
``ad-hoc" way in the sense that while they manage to preserve some particular
aspects of the data, they end up modifying others. Synthetic data approaches
based on the fully conditional specification data synthesis paradigm, on the
other hand, aim to generate new datasets that follow the same joint probability
distribution as the original data. These synthetic data approaches, however,
rely either on parametric statistical models, or non-parametric machine
learning models, which need to fit well the original data in order to generate
credible and useful synthetic data. Another important drawback is that they
tend to perform better when the variables are synthesized in the correct causal
order (i.e., in the same order as the true data generating process), which is
often unknown in practice. To circumvent these issues, we propose a fully
non-parametric and model free perturbative SDC approach that approximates the
joint distribution of the original data via sequential applications of
restricted permutations to the numerical microdata (where the restricted
permutations are guided by the joint distribution of a discretized version of
the data). Empirical comparisons against popular SDC approaches, using both
real and simulated datasets, suggest that the proposed approach is competitive
in terms of the trade-off between confidentiality and data utility.
