# Data Protection and Multi-Database Data-Driven Models
## 4 Experiment and Analysis
For comparison and analysis, note that the range between the maximum and minimum values of the output variable in the training set of this figure (Concrete data set) is 80.27, and therefore, a maximum error of 1.5 represents the 1.8% of the prediction output, and a maximum error of 1.0 represents the 1.2% of the prediction output. For \(k>60\), the error becomes significantly large. As we have explained above, Figure 4 shows the results for MDAV and Mondrian with values of \(k\) up to \(k=50\) and \(k=60\). Larger values of \(k\) produce results with still larger errors. In the case of the Tarragona data set, we show that the range of outputs for the training set is 920,992.0, and then an error of 840 represents 0.91 % of the prediction output. The results of SGD are not displayed; this regression algorithm behaves very badly returning large errors. Figure 5 provides similar results (to Figure 3) for linear regression for different masking methods, and different parameters for the same database, the Concrete data set. Errors in the range [0, 2] are shown. Figure 4: Output model error for the Concrete data set when data are protected using MDAV (**left**) and Mondrian (**right**). Figures represent different protection levels and different numbers of attributes in the database integration process. A larger discrepancy is shown in the figure for 3 common attributes in MDAV and for 2 common attributes in Mondrian. Figure 3: Output model error (**top**) for the Concrete data set when data are protected using Mondrian. Output model error difference (**bottom**) for the Concrete data set when data are protected using Mondrian and when data are not protected. Three different models are considered: linear regression (**left**), kernel ridge (**middle**), and support vector regression (**right**). Figures represent different protection levels and different numbers of attributes in the database integration process. Figure 6 represents the mean and variance for ten executions of the error of the model when data are protected using noise addition. The results correspond to those of the Tarragona data set. Here, the 10 executions are computed on the same training set, but masking noise is applied independently in the 10 runs. A noise parameter equal to zero means no protection. Therefore, for the parameter equal to zero, the 10 executions produce the same model. That is why the standard deviation is zero. This is not the case for non-zero noise. We can see that other parameters have similar variances in the error. In most of the results described in this work, we have not considered multiple partitions of a database into different training and testing data sets, and the effects of this process. This was considered for two masking methods (microaggregation and rank swapping, using five and ten executions) in our previous work [9], and for microaggregation (using 20 executions) for the CASC data set in Figure 7. We have not considered here multiple executions for all the experiments with all the parameterizations, as this is computationally costly, and we preferred to consider instead more masking methods and more parameters. The results reported here using single executions are consistent with those with multiple executions (in both our previous work and in Figure 7). Figure 5: Output model error for the Concrete data set when data are protected using microaggregation (**left**—MDAV and Mondrian), noise addition (**middle**—Gaussian noise and Laplacian noise), and dimensionality reduction (**right**—NMF and SVD-based). Figures represent different protection levels and different numbers of attributes in the database integration process. Figures correspond to linear regression. Figure 6: Mean output model error (**left**) and its variance (**right**), for 10 executions, for the Tarragona data set when data are protected using noise addition. The machine learning model considered is linear regression. Figures represent different protection levels and different numbers of attributes in the database integration process.