## 4 Experiments and Evaluation
### Differential Private Federated Learning on the Public Administration Opinion Data
\begin{table}
\begin{tabular}{l l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Metric**} & \multirow{2}{*}{**Start/End Value**} & \multicolumn{5}{c}{**Opinion Data**} & \multicolumn{5}{c}{**Payroll Data**} \\  & & **2.0** & **4.0** & **6.0** & **8.0** & **10.0** & **2.0** & **4.0** & **6.0** & **8.0** & **10.0** \\ \hline \multirow{2}{*}{Accuracy} & Start & 0.95 & 0.94 & 0.94 & 0.94 & 0.96 & 0.98 & 0.89 & 0.90 & 0.89 & 0.89 \\  & End & 0.95 & 0.95 & 0.95 & 0.96 & 0.96 & 0.89 & 0.90 & 0.89 & 0.89 & 0.91 \\ \hline \multirow{2}{*}{F1 Score} & Start & 0.94 & 0.93 & 0.93 & 0.93 & 0.92 & 0.99 & 0.93 & 0.89 & 0.86 & 0.85 \\  & End & 0.94 & 0.94 & 0.93 & 0.93 & 0.92 & 0.93 & 0.89 & 0.86 & 0.85 & 0.85 \\ \hline \multirow{2}{*}{epsilon (c)} & Start & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 \\  & End & 0.23 & 0.08 & 0.04 & 0.02 & 0.01 & 0.14 & 0.04 & 0.02 & 0.01 & 0.004 \\ \hline \multirow{2}{*}{RDP} & Start & 45.29 & 62.86 & 63.00 & 100.14 & 118.71 & 52.57 & 63.00 & 90.86 & 128.00 & 128.00 \\  & End & 14.43 & 25.00 & 33.29 & 40.14 & 46.29 & 19.14 & 32.43 & 42.43 & 50.43 & 56.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: DPFL model performance (accuracy, F1 score) and privacy quantification (RDP, epsilon (\(\epsilon\))) results (noise multipliers: 2–10). However, introducing noise into noise multiplier 2 or greater results in a consistent decrease in accuracy and F1 scores for all clients, indicating stronger resilience against MIAs (Table 4). For example, in the opinion data set, in noise multiplier 2, the accuracy is reduced to approximately 91% and the F1 score falls to approximately 89%. The results show a progressive improvement in privacy protection for noise multipliers 4, 6, 8, and 10. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Client 1**} & \multicolumn{3}{c}{**Client 2**} & \multicolumn{3}{c}{**Client 3**} & \multicolumn{3}{c}{**Client 4**} & \multicolumn{3}{c}{**Client 5**} & \multicolumn{3}{c}{**Client 6**} & \multicolumn{3}{c}{**Client 7**} \\ \cline{2-13}
**Noise Multiplier** & **Acc** & **F1** & **Acc** & **F1** & **Acc** & **F1** & **Acc** & **F1** & **Acc** & **F1** & **Acc** & **F1** & **Acc** & **F1** \\  & & **Score** & & **Score** & & **Score** & & & **Score** & & & **Score** & & **Score** & & **Score** \\ \hline
0 (Un-noisy Model) & 0.95 & 0.94 & 0.95 & 0.94 & 0.95 & 0.94 & 0.95 & 0.95 & 0.95 & 0.94 & 0.96 & 0.95 & 0.95 & 0.95 \\ \hline
2 & 0.91 & 0.89 & 0.89 & 0.89 & 0.89 & 0.89 & 0.90 & 0.89 & 0.91 & 0.89 & 0.90 & 0.89 & 0.89 & 0.89 \\
4 & 0.79 & 0.79 & 0.79 & 0.79 & 0.79 & 0.78 & 0.79 & 0.78 & 0.78 & 0.79 & 0.78 & 0.79 & 0.79 & 0.79 \\
6 & 0.67 & 0.72 & 0.69 & 0.69 & 0.69 & 0.69 & 0.72 & 0.61 & 0.70 & 0.67 & 0.72 & 0.63 & 0.73 & 0.59 \\
8 & 0.62 & 0.51 & 0.62 & 0.50 & 0.63 & 0.43 & 0.61 & 0.53 & 0.62 & 0.49 & 0.59 & 0.59 & 0.59 & 0.58 \\
10 & 0.54 & 0.23 & 0.47 & 0.56 & 0.45 & 0.60 & 0.51 & 0.45 & 0.49 & 0.48 & 0.46 & 0.58 & 0.46 & 0.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Opinion data: un-noisy and noisy MIA models’ performance (success rates). Figure 4: Opinion data: inference attack F1 score success rates of un-noisy and noisy model. Lower rates indicate stronger privacy against attacks. Colors/bars represent different noise levels. Figure 3: Opinion data: epsilon (\(\epsilon\)) and Renyi differential privacy in relation with round number and noise multipliers.