The creation of a mathematical framework for evaluating the utility and the risks of disclosure when anonymizing data is the goal of this paper. A balance between information loss and the risk of disclosure needs to be maintained.

The paper attempts to model the discrepancy of information loss when anonymizing data, using the concept of mutual information. Domingo-Ferrer and Rebollo-Monedero discuss the advantage of adopting the metric of mutual information over other metrics--such as the mean squared errors and correlations--in modeling the information loss. They also propose four models for attaining the optimal point of balance between information loss and disclosure risk.

Applying the concept of mutual information in anonymizing data is a novel idea. The entropy-based mutual information metric is capable of characterizing the discrepancy between the distributions of two datasets. The paper also makes a valuable contribution toward balancing the trade-off between information loss and disclosure risk in the framework of the Lagrangian convexity model.

However, the authors only provide a high-level discussion on measuring the utility and risk of anonymized data. They assume that the distributions of the datasets have been obtained; methods for measuring these should have been discussed, in order to evaluate the effectiveness of the four models proposed. The paper also lacks an in-depth discussion of the process of anonymizing data that is driven by the process of optimization. The authors also should have provided an optimization-based algorithm for anonymizing data.