# Comparative Analysis of Local Differential Privacy Schemes in Healthcare Datasets
## 4 Experiments
### Results  
We select randomly one hundred times \(k\)-way joint probability attributes. To analyze the joint probability distributions, we use the AVD to quantify the difference between real and computed data; according to LOPUB [6] and LOCOP [10], it is defined as  
\[AVD=\frac{1}{2}\sum_{\omega\in\Omega}|P(\omega)-Q(\omega)|. \tag{8}\]  
The results depicted in Figure 3 pertain to six distinct datasets: Nursery, NHANES, Massachusetts, MSFimu, Diabetes, and Cirrhosis. We have chosen to present their results due to the datasets showcasing significant differences in terms of size, attribute composition, and AAR. These variations in size, attribute count, and AAR underscore the diverse nature and potential applications of each dataset across various domains, including healthcare, demographics, and machine learning research. Readers are encouraged to explore the results of the fifteen datasets available in this study by visiting the website [[https://www.kikn.fms.meijii.ac.jp/~andres/BRR.html](https://www.kikn.fms.meijii.ac.jp/~andres/BRR.html)]([https://www.kikn.fms.meijii.ac.jp/~andres/BRR.html](https://www.kikn.fms.meijii.ac.jp/~andres/BRR.html)), accessed on 27 February 2024. The website also presents a comparison between AVD and AAR for all datasets using different values of \(\epsilon\) within the range of \([0.1,1]\), along with the \(k\)-way joint probability distribution. Figure 4 illustrates the outcomes for \(\epsilon=0.1\) and \(k=2,3,4,5\). We have chosen this specific privacy budget as it provides a robust level of privacy for the users. Figure 3 presents the results of the experiments conducted on the six datasets using three algorithms: LOPUB, LOCOP, and BRR. The Y-axis illustrates the AVD between the original and computed data, with lower values indicating superior performance. On the X-axis, the privacy budget is depicted, where lower values signify a higher level of privacy. The four columns display results for different \(k\)-way settings, specifically \(k=2,3,4,5\). The shaded blue, green, and red areas represent the standard deviations of LOPUB, LOCOP, and BRR, respectively. \begin{table}
\begin{tabular}{c c c c} \hline
**Dataset** & **\# Users** & **\# Attributes** & **AAR** \\ \hline Nursery & 12,960 & 9 & 0.0240 \\ Lung Cancer & 53,427 & 5 & 0.0411 \\ Stroke & 40,910 & 11 & 0.0645 \\ NHANES & 4189 & 10 & 0.0747 \\ Bank & 45,211 & 17 & 0.0919 \\ National & 27,253 & 24 & 0.1002 \\ Massachusetts & 7634 & 24 & 0.1006 \\ Texas & 9276 & 24 & 0.1035 \\ MS FIMU & 88,935 & 6 & 0.1068 \\ Adults & 45,222 & 10 & 0.1088 \\ Hypertension & 26,083 & 14 & 0.1237 \\ Skin Cancer & 10,015 & 5 & 0.1268 \\ Diabetes & 70,692 & 18 & 0.1334 \\ US CENSUS & 245,828 & 68 & 0.1607 \\ Cirrhosis & 418 & 17 & 0.2790 \\ \hline \end{tabular}
\end{table} 
Table 3: Datasets characteristics. The findings indicate that, in terms of AVD, BRR consistently outperforms LOPUB and LOCOP. Across all six datasets, BRR achieves lower AVD values than LOPUB and LOCOP at various privacy budgets. This implies that BRR can attain better accuracy while preserving greater privacy compared to the other two algorithms. Overall, the standard deviations are similar for the three algorithms. Moreover, the results reveal an overall  
Figure 3: AVD vs. privacy budget (\(\epsilon\)) per attribute. The best value of AVD is close to zero as is the best privacy budget value (\(\epsilon\)). enhancement in the performance of all three algorithms as the privacy budget increases. This is attributed to a larger privacy budget allowing users to incorporate less noise for data protection. However, it is crucial to acknowledge that the algorithm performance may vary depending on the dataset. For example, BRR significantly outperforms LOPUB and LOCOP on the Nursery dataset, while the distinction is less pronounced on the Cirrhosis dataset, potentially due to AAR. A high AAR value suggests a strong correlation between attributes, posing a risk of information extraction from one attribute to another or causing noise propagation to other attributes.