# QoE Modeling on Split Features with Distributed Deep Learning
## 6 Results
### Vertical Federated Learning (VFL)  
In this section, we present results from the main proposed approach, _Vertical Federated Learning_ (\(vFL\)) that enables model training collaboratively without manual effort such as adjusting weights and selecting common features as in \(DEL\) as this is done during the iterative adjustment of the neuron weights during training. We compare \(vFL\) with the reference _Isolated_ and _Fully Centralized_ settings. The learning curves of the workers during the training phase on the training dataset, which show the F1-score accuracy on the _training set_, are depicted over the 4000 federation rounds in Figures 12 and 13 when the feature _meanBitrate_ is included and excluded in the feature set, respectively. The mean values of the accuracy values are given together with the standard error around the mean (with 95 th percentile upper and lower bounds) values on the corresponding training round are given via 'x' marker. The blue curve depicts the G0 F1-score accuracy over the rounds; the orange curve depicts the G1 F1-score accuracy over the rounds; red curve depicts the \(vFL\) F1-score accuracy over the rounds; and the green curve depicts the reference _Fully Centralized_ F1-score accuracy over the rounds. All experiments are conducted via the same number of rounds, (where one round consists of one forward-pass and backward-propagation), and we consider 4000 rounds as the average model saturation point. We evaluate and compare model performances after the models reaches the saturation. The learning rate of each NN model was set to 0.01.  
Indeed, if a worker has a strong indicator feature for MOS estimation such as _meanBitrate_ (located at index position 8), it enables the G1 to perform almost as good as the \(vFL\), while G0 benefits from \(vFL\) setting. This case is depicted in Figure 12a-c, when the split index is set to 2, 4, and 6, respectively. Although the G0 F1-score accuracy increases with the number of features (i.e., with the split index) in G0 as depicted from left to right, this increase is not enough to reach the level of \(vFL\) accuracy, which shows that G0 would still significantly benefit from \(vFL\).  
We repeat the experiments when the _meanBitrate_ feature is removed from the dataset, and the corresponding results are given in Figure 13. In this case, if the split index is set to a value such as index 4, such that features are distributed in a more balanced manner, then the benefit of \(vFL\) is revealed clearly on both groups; G0 and G1 as given in Figure 13b. This is the scenario where both groups (workers) have equal number of model indicator features,where none of them dominates alone. Once the groups collaborate via \(vFL\), they both benefit each other yielding a significant increase in the F1-score accuracy values. Similarly when the split feature is set to 6, both groups benefit from \(vFL\) as given in Figure 12(c), although not as much as in the case when the split index is 4.  
Figure 12: \(vFL\) when all features are used and split into two workers.  
Figure 13: \(vFL\) when all features without meanBitrate are used and split into two workers.