# Uncertainty Flow Facilitates Zero-Shot Multi-Label Learning in Affective Facial Analysis
## 4 Experiment
### Results & Discussion
#### 4.4.1 Model Comparison  
Ruling out the factors of prior types and prediction related uncertainty indexes, the empirical comparison between **Uncertainty Flow** framework and the alternatives demonstrated mixed results, illustrated in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Candidate Models** & **Hamming-Loss** & **Converge-Loss** & **Ranking-Loss** & **F-Score** & **Average Precision** & **Source** \\ \hline \multicolumn{6}{c}{Conventional Multi-Label Models} \\ \hline MLkNN & 0.286 & 7.000 & 0.950 & 0.990 & 0.346 & [14] \\ ML-ARAM & 0.374 & 6.670 & 0.801 & 0.264 & 0.369 & [13] \\ Binary Relevance & **0.275** & 7.00 & 1.000 & 0.263 & 0.340 & [38] \\ Label Powerset & 0.328 & 6.940 & 0.837 & 0.215 & 0.370 & [39] \\ \hline \multicolumn{6}{c}{Multi-Label Compatible Neural Networks} \\ \hline ML-FNN & 0.402 & 6.700 & 0.761 & 0.282 & 0.376 & [40] \\ ML-CNN & 0.387 & 6.600 & 0.733 & 0.3108 & 0.384 & [41] \\ \hline \multicolumn{6}{c}{Uncertainty Flow - Bayesian Neural Networks} \\ \hline BNN-normal-soft & 0.404 & 6.500 & 0.75 & 0.279 & 0.360 & This research \\ BNN-normal-pure & 0.382 & 6.500 & **0.723** & 0.318 & 0.389 & This research \\ BNN-normal-plus & 0.402 & 6.673 & 0.759 & 0.282 & 0.525 & This research \\ BNN-uniform-soft & 0.414 & 6.750 & 0.7816 & 0.302 & 0.353 & This research \\ BNN-uniform-pure & 0.385 & 6.450 & 0.723 & 0.330 & 0.389 & This research \\ BNN-uniform-plus & 0.404 & 6.450 & 0.765 & 0.310 & 0.530 & This research \\ BNN-cauchy-soft & 0.400 & 6.7 & 0.759 & 0.285 & 0.378 & This research \\ BNN-cauchy-pure & 0.382 & 6.525 & 0.727 & 0.312 & 0.402 & This research \\ \multicolumn{6}{c}{**BNN-cauchy-plus**} \\ \hline \multicolumn{6}{c}{Uncertainty Flow - Bayesian Convolutional Neural Networks} \\ \hline BCNN-normal-soft & 0.421 & 6.750 & 0.791 & 0.250 & 0.385 & This research \\ BCNN-normal-pure & 0.384 & 6.700 & 0.737 & 0.319 & 0.449 & This research \\ BCNN-normal-plus & 0.400 & 6.675 & 0.751 & 0.288 & 0.561 & This research \\ BCNN-uniform-soft & 0.403 & 6.675 & 0.762 & 0.282 & 0.421 & This research \\ BCNN-uniform-pure & 0.404 & 6.800 & 0.769 & 0.279 & 0.311 & This research \\ BCNN-uniform-plus & 0.387 & 6.725 & 0.736 & 0.310 & 0.527 & This research \\ BCNN-cauchy-soft & 0.401 & 6.675 & 0.760 & 0.285 & 0.416 & This research \\ BCNN-cauchy-pure & 0.396 & 6.800 & 0.753 & **0.322** & 0.390 & This research \\ BCNN-cauchy-plus** & 0.401 & 6.75 & 0.758 & 0.285 & **0.576** & This research \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model Comparison in Various Multi-label Evaluation Metrics.  
Previous findings from [11] and [6] stated that it is practical difficult to observe a single model or algorithm, which is competitive enough to beat others in every multi-label evaluation metric. Hence, it is imperative to investigate each loss metric independently. Focusing on _Hamming-Loss_ (Hamming-ACC = 1 - Hamming loss), interestingly, the conventional multi-label learning models are particular good in minimising this type of loss. However, indicated in _Converge-Loss_ and _Ranking-Loss_, both **Uncertainty Flow** and multi-label compatible neural networks, e.g., ML-FNN and ML-CNN are superior than the conventional multi-label learning alternatives.  
Under two precision related metrics, e.g., _F-score_ and _average precision_, with the help from a weakly informative prior, e.g., uniform or Cauchy prior, and an advanced prediction related uncertainty indexes, e.g., **pure uncertainty**, or **uncertainty plus**, both BNN and BCNN, exhibited clear performance advantage over their alternatives, e.g., ML-FNN, ML-CNN and conventional multi-label models. Especially on the metric of _average Precision_, the nontrivial performance enhancement, i.e., over 20% accuracy increase, demonstrated the superior discriminability that tags to our proposed **Uncertainty Flow**. Moreover, comparing the performance between BNN and BCNN, the convolutional architecture, e.g., BCNN, should be credited for overall performance improvement.