Releasable inner cell frequencies by post-processing protected tabular data

and Paper The microdata underlying tabular frequency data can be represented by the inner frequency table obtained by crossing all the main dimensional variables. This paper will discuss approaches to postprocessing the results of tabular SDC techniques to obtain releasable inner frequencies, which may not be whole numbers. As suggested in a recent publication and implemented in the r-package RegSDC, suppressed cells may be replaced by decimal numbers, in a way so that they add correctly up to non-supressed marginals. A similar method could be used in cases without cell suppression, but where only some marginals are considered releasable. This method (Method A) can be viewed as ordinary regression, modified to handle collinearity, with the inner cells as the unknown parameters and with the releasable marginals as response observations. Method A can also be interpreted as linear calibration weighting. An improvement of this approach is to ensure non-negative values by applying nonnegative least squares with ridge penalty (Method B). A more natural choice in this case, would be to obtain inner frequencies as fitted values from log-linear modelling. Considering situations where the marginals are perturbed in a non-additive way, ordinary log-linear modelling is not possible, but Method B is useful. Log-linear fitting may be performed afterwards to obtain results in in accordance with such modelling assumptions. Another situation is when only some of the releasable marginals are perturbed. Then, it is advantageous to modify Method B by incorporating weights (Method C). The perturbed marginals are weighted down, so that the resulting inner frequencies add up almost exactly to the non-perturbed marginals. The methodology is applicable when the marginals are perturbed by Laplace noise to ensure differential privacy. Although, in this case, one may consider least absolute deviation instead of least squares. The generated frequencies serve several purposes: They can be used internally or published directly. Additivity of marginals can be restored. One can also use the results to generate public microdata. Then, all frequencies must be whole numbers. A possibility is to round up or down by comparing the decimals to draws from the uniform distribution. This is an alternative to synthetic data drawn as a multinomial sample according to cell probabilities, as in the r-package synthpop. The methodology is tested using example data of various size and complexity. For an efficient implementation, making use of the r-package glmnet seems promising. Releasable inner cell frequencies by post-processing protected tabular data Øyvind Langsrud∗ ∗ Statistics Norway, Department of methodology and data collection, Oyvind.Langsrud@ssb.no, github.com/olangsrud Abstract. The microdata underlying tabular frequency data can be represented by the inner frequency table obtained by crossing all the main dimensional variables. This paper will discuss approaches to post-processing the results of tabular SDC techniques to obtain releasable inner frequencies, which may not be whole numbers. As suggested in a recent publication and implemented in the r-package RegSDC, suppressed cells may be replaced by decimal numbers, in a way so that they add correctly up to non-supressed margins. A similar method could be used in cases without cell suppression, but where only some margins are considered releasable. This method (Method A) can be viewed as ordinary regression, modified to handle collinearity, with the inner cells as the unknown parameters and with the releasable margins as response observations. Method A can also be interpreted as linear calibration weighting. An improvement of this approach is to ensure non-negative values by applying non-negative least squares with ridge penalty (Method B). A more natural choice in this case, would be to obtain inner frequencies as fitted values from log-linear modelling. Considering situations where the margins are perturbed in a non-additive way, ordinary log-linear modelling is not possible, but Method B is useful. Log-linear fitting may be performed afterwards to obtain results in in accordance with such modelling assumptions. Another situation is when only some of the releasable margins are perturbed. Then, it is advantageous to modify Method B by incorporating weights (Method C). The perturbed margins are weighted down, so that the resulting inner frequencies add up almost exactly to the non-perturbed margins. The methodology is applicable when the margins are perturbed by Laplace noise to ensure differential privacy. Although, in this case, one may consider least absolute deviation instead of least squares. The generated frequencies serve several purposes: They can be used internally or published directly. Additivity of margins can be restored. One can also use the results to generate public microdata. Then, all frequencies must be whole numbers. A possibility is to round up or down by comparing the decimals to draws from the uniform distribution. This is an alternative to synthetic data drawn as a multinomial sample according to cell probabilities, as in the r-package synthpop. The methodology is tested using example data of various size and complexity. For an efficient implementation, making use of the r-package glmnet seems promising. The microdata underlying tabular frequency data can be represented by the inner frequency table obtained by crossing all the main dimensional variables. This paper will discuss approaches to post-processing the results of tabular SDC techniques to obtain releasable inner frequencies, which may not be whole numbers. As suggested in a recent publication and implemented in the r-package RegSDC, suppressed cells may be replaced by decimal numbers, in a way so that they add correctly up to non-supressed margins. A similar method could be used in cases without cell suppression, but where only some margins are considered releasable. This method (Method A) can be viewed as ordinary regression, modified to handle collinearity, with the inner cells as the unknown parameters and with the releasable margins as response observations. Method A can also be interpreted as linear calibration weighting. An improvement of this approach is to ensure non-negative values by applying non-negative least squares with ridge penalty (Method B). A more natural choice in this case, would be to obtain inner frequencies as fitted values from log-linear modelling. Considering situations where the margins are perturbed in a non-additive way, ordinary log-linear modelling is not possible, but Method B is useful. Log-linear fitting may be performed afterwards to obtain results in in accordance with such modelling assumptions. Another situation is when only some of the releasable margins are perturbed. Then, it is advantageous to modify Method B by incorporating weights (Method C). The perturbed margins are weighted down, so that the resulting inner frequencies add up almost exactly to the non-perturbed margins. The methodology is applicable when the margins are perturbed by Laplace noise to ensure differential privacy. Although, in this case, one may consider least absolute deviation instead of least squares. The generated frequencies serve several purposes: They can be used internally or published directly. Additivity of margins can be restored. One can also use the results to generate public microdata. Then, all frequencies must be whole numbers. A possibility is to round up or down by comparing the decimals to draws from the uniform distribution. This is an alternative to synthetic data drawn as a multinomial sample according to cell probabilities, as in the r-package synthpop. The methodology is tested using example data of various size and complexity. For an efficient implementation, making use of the r-package glmnet seems promising.