# Secure and Efficient Federated Gradient Boosting Decision Trees
## 6 Experiments
### Experimental Results
#### 6.2.2 Performance Impact of Participants' Data Imbalance Ratio  
In the practical use of federation learning, the amount of data provided by federated participants is often different. Therefore, federated learning algorithms should be robust to unbalanced distributions of data. This experiment used the partitioning method from a previous study [48] to assign skewed local datasets to the participants. We set the number of participants to 2 and adjust the imbalance ratio \(\theta\) from 60% to 80%. One of the participants received \(\frac{\theta*N_{\text{data}0}}{2}\) instances with label 0, and \(\frac{\theta*N_{\text{data}1}}{2}\) instances with label 1, and the other participant received the opposite.  
The experimental results are shown in Table 7 and Figure 5. We can observe that the performance of all models decreases with the increase in imbalance ratio \(\theta\). Secondly, the performance of SeFB is able to approach Non. Thirdly, in all cases, the performance of TFL, eFL-Boost and Independent tends to be lower, while the performance of SeFB is always better than them. Thus, SeFB is able to achieve performance enhancement through FL, even when the data of the participants are not balanced.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Schemes**} & \multicolumn{8}{c}{**F1-Score**} & \multicolumn{8}{c}{**ROC-AUC**} \\ \cline{3-11}  & & **2** & **4** & **6** & **8** & **10** & **2** & **4** & **6** & **8** & **10** \\ \hline \multirow{4}{*}{Credit 1} & Non & 0.812 & 0.826 & 0.843 & 0.857 & 0.861 & 0.972 & 0.975 & 0.975 & 0.978 & 0.980 \\  & Independent & 0.763 & 0.769 & 0.768 & 0.769 & 0.751 & 0.963 & 0.963 & 0.965 & 0.966 & 0.966 \\  & TFL & 0.792 & 0.797 & 0.799 & 0.805 & 0.814 & 0.966 & 0.972 & 0.974 & 0.975 & 0.976 \\  & eFL-Boost & 0.801 & 0.820 & 0.839 & 0.841 & 0.843 & 0.970 & 0.972 & 0.973 & 0.974 & 0.975 \\  & SeFB & 0.811 & 0.824 & 0.841 & 0.851 & 0.858 & 0.971 & 0.974 & 0.975 & 0.977 & 0.979 \\ \hline \multirow{4}{*}{Credit 2} & Non & 0.901 & 0.904 & 0.906 & 0.908 & 0.910 & 0.922 & 0.925 & 0.927 & 0.930 & 0.934 \\  & Independent & 0.882 & 0.891 & 0.893 & 0.893 & 0.894 & 0.911 & 0.912 & 0.913 & 0.914 & 0.916 \\  & TFL & 0.889 & 0.891 & 0.897 & 0.900 & 0.902 & 0.916 & 0.917 & 0.919 & 0.922 & 0.928 \\  & eFL-Boost & 0.900 & 0.902 & 0.904 & 0.906 & 0.907 & 0.920 & 0.923 & 0.925 & 0.927 & 0.931 \\  & SeFB & 0.901 & 0.903 & 0.906 & 0.908 & 0.910 & 0.922 & 0.924 & 0.926 & 0.930 & 0.933 \\ \hline \multirow{4}{*}{Adult} & Non & 0.722 & 0.731 & 0.740 & 0.748 & 0.767 & 0.888 & 0.900 & 0.902 & 0.906 & 0.911 \\  & Independent & 0.662 & 0.671 & 0.678 & 0.683 & 0.698 & 0.843 & 0.844 & 0.845 & 0.845 & 0.847 \\ \cline{1-1}  & TFL & 0.689 & 0.693 & 0.710 & 0.718 & 0.732 & 0.873 & 0.875 & 0.877 & 0.888 & 0.896 \\ \cline{1-1}  & eFL-Boost & 0.718 & 0.724 & 0.733 & 0.740 & 0.752 & 0.883 & 0.885 & 0.889 & 0.899 & 0.903 \\ \cline{1-1}  & SeFB & 0.721 & 0.729 & 0.736 & 0.745 & 0.763 & 0.885 & 0.888 & 0.897 & 0.902 & 0.909 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance impact of the number of data participants.  
Figure 4: Impact of number of participants on Test Errors. (**a**) Credit 1 dataset, (**b**) Credit 2 dataset, (**c**) Adult dataset.  
Figure 5 shows the test errors with participants' data imbalance ratio, where the horizontal coordinate indicates the imbalance ratio \(\theta\). With the increase in \(\theta\), SeFB has better prediction performance than Independent, TFL and eFL-Boost.