## 4 Results
### FMTL Framework Performance  
To evaluate the effectiveness of our proposed FMTL framework, we conducted comparative experiments from two perspectives. First, as illustrated in Figure 6, we examined the impact of the federated learning strategy by comparing three settings: (a) Single: Models are trained and tested independently on each client's local data. (b) Mix: Data from all clients is pooled together in a centralized setting to train a shared global model. (c) FedAvg: A standard federated averaging algorithm used to simulate distributed collaborative learning without data sharing in this study. As summarized in Table 5, under simulated multi-client conditions, the FMTL framework achieved the highest accuracy for both sleep staging and SDB severity classification, demonstrating its ability to provide reliable diagnostic performance without compromising data privacy. Specifically, the APPLES client shows an increase in accuracy from 78.2% (Single) and 83.5% (Mix) to 85.3% (FMTL), and an MF1 improvement from 69.1% (Single) and 72.2% (Mix) to 76.7% (FMTL). Similar trends are observed for SHHS and HMC clients, highlighting the superior generalization ability of FMTL even in the presence of data heterogeneity. For OSA severity classification, the FMTL model also achieves the best results, with the highest accuracy and MAUC on all clients. For instance, on the HMC dataset, the accuracy rises from 82.5% (Single) and 83.1% (Mix) to 85.4% (FMTL), while the MAUC improves from 85.1 (Single) and 86.7 (Mix) to 89.9 (FMTL). These gains confirm that the federated multi-task learning framework can effectively leverage distributed data to boost model robustness and classification power, while preserving local data privacy.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Client (Dataset)**} & \multicolumn{8}{c}{**Sleep Stages (\%)**} & \multicolumn{8}{c}{**OSA Severity (\%)**} \\ \cline{2-11}  & **Recall** & **Specificity** & **Acc** & **MF1** & **MGm** & \(\mathbf{\kappa}\) & **Recall** & **Specificity** & **Acc** & **MF1** & **MAUC** \\ \hline \multirow{4}{*}{APPLES} & Single & 66.8 & 80.2 & 78.2 & 69.1 & 79.9 & 0.68 & 67.5 & 82.1 & 70.0 & 69.2 & 78.5 \\  & Mix & 71.0 & 85.3 & 83.5 & 72.2 & 81.6 & 0.69 & 69.4 & 88.0 & 74.2 & 70.8 & 79.9 \\  & FMTL & 74.7 & 96.1 & 85.3 & 76.7 & 83.7 & 0.71 & 73.4 & 91.3 & 79.2 & 74.6 & 82.4 \\ \cline{1-1}  & Single & 76.4 & 94.5 & 78.9 & 75.2 & 84.3 & 0.78 & 77.2 & 81.9 & 78.4 & 77.2 & 80.6 \\ \cline{1-1}  & Mix & 81.4 & 95.7 & 85.1 & 79.4 & 88.2 & 0.82 & 82.1 & 94.4 & 83.9 & 83.5 & 85.1 \\ \cline{1-1}  & FMTL & 82.5 & 96.4 & 87.1 & 81.5 & 89.0 & 0.86 & 82.7 & 94.5 & 84.5 & 83.8 & 88.6 \\ \cline{1-1}  & Single & 68.2 & 84.1 & 72.5 & 73.9 & 80.6 & 0.69 & 79.4 & 83.9 & 82.5 & 83.8 & 85.1 \\ \cline{1-1}  & Mix & 73.1 & 90.5 & 77.4 & 73.2 & 82.1 & 0.70 & 80.0 & 88.2 & 83.1 & 83.9 & 86.7 \\ \cline{1-1}  & FMTL & 76.7 & 94.6 & 79.3 & 77.0 & 85.0 & 0.72 & 84.8 & 95.0 & 85.4 & 85.0 & 89.9 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The performance of three datasets for sleep SDB severity classification task by using FMTL framework.  
Figure 5: SDB severity classification confusion matrixes of the three clients (APPLES, SHHS_rest, and HMC dataset).