# Hybrid Uncertainty Metrics-Based Privacy-Preserving Alternating Multimodal Representation Learning
## 4 Results and Discussion
### Main Result for the PAMRL  
To evaluate the performance of the PAMRL model, we compared two configurations, the MLA model [6] and the PAMRL model, to ensure user-level differential privacy. To achieve robust privacy guarantees while maintaining model utility, we systematically selected DPSGD hyperparameters--gradient clipping threshold (\(C\)) and noise standard deviation (\(\delta\))--based on empirical gradient norm analysis and established DP-SGD practices [13; 24]. Performance was assessed using accuracy, recall, precision, F1 score, Expected Calibration Error (ECE), and Low Confidence Accuracy (ConfAcc_Low) over 100 training epochs. The results, visualized in Figures 2-5, demonstrate the PAMRL model's efficacy in privacy preservation through DPSGD. The best results of all models on two datasets are reported in Table 1.  
**Accuracy-Related Metrics**: Table 1 reveals that for accuracy-related metrics (accuracy, precision, F1-score, recall), MLA outperforms PAMRL on both CREMA-D (accuracy: 72.21%, precision: 77.11%, recall: 75.41%, F1-score: 69.45%) and MVSA (accuracy: 62.23%, precision: 72.65%, recall: 76.23%, F1-score: 71.67%), while PAMRL with \(\epsilon=1\) (CREMA-D: accuracy 62.58%, F1-score 53.35%; MVSA: accuracy 55.56%, F1-score 54.42%) and \(\epsilon=2\) (CREMA-D: accuracy 65.69%, F1-score 62.24%; MVSA: accuracy 58.45%, F1-score 58.65%) shows a performance overhead due to differential privacy. This indicates that DP introduces a trade-off, reducing classification performance to prioritize privacy, with \(\epsilon=2\) offering better utility than \(\epsilon=1\). This reflects PAMRL's conservative performance approach, sacrificing some accuracy to ensure privacy protection while maintaining practical utility for real-world tasks. This performance supports PAMRL's framework by demonstrating its ability to protect sensitive data via DP while still achieving usable accuracy, making it suitable for privacy-sensitive multimodal applications like sentiment analysis. **Confidence-Related Metrics**: For confidence-related metrics (ECE, ConfAcc_Low), Table 1 shows that MLA has lower ECE (CREMA-D: 5.54%, MVSA: 4.76%) but limited ConfAcc_Low (CREMA-D: 46.75%, MVSA: 51.54%), while PAMRL with \(\epsilon=1\) (CREMA-D: ECE 18.34%, ConfAcc_Low 30.12%; MVSA: ECE 9.45%, ConfAcc_Low 40.16%) and \(\epsilon=2\) (CREMA-D: ECE 14.35%, ConfAcc_Low 32.34%; MVSA: ECE 6.43%, ConfAcc_Low 45.87%) exhibits higher ECE but improved ConfAcc_Low with \(\epsilon=2\), indicating better calibration and low-confidence prediction reliability under DP constraints. This suggests that PAMRL trades off calibration tightness for enhanced prediction stability, especially with a relaxed privacy budget (\(\epsilon=2\)). This reflects PAMRL's robustness in handling uncertain predictions, a critical aspect of reliable multimodal learning in noisy scenarios. Such performance supports PAMRL's framework by validating its mixed uncertainty metrics, which address modality laziness by ensuring balanced cross-modal fusion, enhancing model reliability for applications like emotion recognition in privacy-sensitive domains. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **Model** & **Accuracy** & **Precision** & **F1 Score** & **Recall** & **ECE** & **ConfAcc_Low** \\ \hline \multirow{3}{*}{CREMAD} & MLA [6] & 72.21\% & 77.11\% & 69.45\% & 75.41\% & 5.54\% & 46.75\% \\  & PAMRL (\(\epsilon=1\)) & 62.58\% & 68.54\% & 53.35\% & 67.78\% & 18.34\% & 30.12\% \\  & PAMRL (\(\epsilon=2\)) & 65.69\% & 74.65\% & 62.24\% & 69.56\% & 14.35\% & 32.34\% \\ \hline \multirow{3}{*}{MVSA} & MLA [6] & 62.23\% & 72.65\% & 71.67\% & 76.23\% & 4.76\% & 51.54\% \\  & PAMRL (\(\epsilon=1\)) & 55.56\% & 61.48\% & 54.42\% & 61.94\% & 9.45\% & 40.16\% \\ \cline{1-1}  & PAMRL (\(\epsilon=2\)) & 58.45\% & 63.45\% & 58.65\% & 64.34\% & 6.43\% & 45.87\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The overhead of differential privacy in PAMRL vs. MLA’s best results on CREMA-D and MVSA datasets. Figure 4: _Cont_.