# Comparative Analysis of Local Differential Privacy Schemes in Healthcare Datasets
## 4 Experiments
### Results
This, in turn, leads to a further decline in data utility. The propagation of noise makes it difficult to accurately estimate joint probability distributions, as shown in Figure 3.  
Figure 5 shows the results of the experiments on the six datasets using two regression algorithms: LASSO and BRR. The Y-axis shows the R-squared between the original and the estimated data, where a value close to one indicates better performance. The X-axis shows the privacy budget, where lower values indicate more privacy. The four columns display results for different \(k\)-way joint probability distribution settings, specifically \(k=2,3,4,5\). The shaded blue and red areas represent the standard deviation of LASSO and BRR, respectively. BRR generally outperforms LASSO in terms of R-squared. Across all six datasets and privacy budgets, BRR consistently achieves higher R-squared values compared to LASSO. This indicates that BRR effectively handles multicollinearity, even when privacy requirements are stringent. Additionally, it is worth noting that, overall, the standard deviation of LASSO is typically higher than that of BRR. The performance of AVD improves with a decreased privacy budget. As the privacy budget decreases (moving towards the right on the X-axis), the R-squared values for both algorithms increase. This is because a lower privacy budget allows the algorithms to use more information without noise for estimation, leading to better preservation of attributes relationships. BRR's advantage is most pronounced on the Nursery and MS FIMU datasets. For these datasets, BRR achieves significantly higher R-squared values compared to LASSO, even at low privacy budgets. Figure 4: AVD vs. dataset average attribute correlation. The difference between BRR and LASSO is smaller on the Cirrhosis dataset. On this dataset, BRR's R-squared values are only slightly higher than those of LASSO, particularly at \(k=5\). Figure 4 shows the results of the experiments comparing the performance of LOPUB, LOCOP, and BRR on fifteen datasets. The Y-axis shows the A  
Figure 5: R-squared (\(R2\)) vs. privacy budget (\(\epsilon\)) per attribute. The best value of R-squared is one, and the best privacy budget (\(\epsilon\)) is close to zero. and the estimated data, where a value close to zero indicates better performance. The X-axis shows the AAR, where lower values indicate less correlation between attributes. The charts display results for different \(k\)-way joint probability distribution settings, specifically \(k=2,3,4,5\) with a privacy budget set as \(\epsilon=0.1\). Figure 4 shows that BRR generally outperforms LOPUB and LOCOP in terms of utility (AVD). Across \(k=4,5\) settings and for most of the datasets, BRR achieves lower AVD values compared to the other two algorithms. This means that BRR can estimate the data more accurately while preserving more privacy than LOPUB and LOCOP. The performance of all three algorithms varies depending on the dataset. Considering the Nursery and Cirrhosis datasets, which have the lowest and highest AAR values, respectively, in the Nursery dataset, as \(k\) increases, BRR significantly outperforms both LOPUB and BRR. In the Cirrhosis dataset, as \(k\) increases, the three algorithms exhibit similar values. This suggests that with an increase in \(k\), more highly correlated attributes become available to estimate the joint probability distribution. In Figure 4, the chart in the bottom right, when \(k=5\), illustrates how the performances of all three algorithms become similar as highly correlated attributes become available to estimate the joint probability distribution. For some datasets, such as the Nursery and Bank datasets, BRR achieves significantly lower AVD values compared to the other algorithms. However, for other datasets, such as the Cirrhosis and USCENSUS datasets, the differences between the algorithms are smaller. BRR's advantage is most pronounced for \(k=4,5\). For these settings, BRR consistently achieves the lowest AVD values across most datasets. LOPUB generally performs worse than LOCOP and BRR.