# Parallel Bidirectionally Pretrained Taggers as Feature Generators
## 3 Results
\begin{table}
\begin{tabular}{c|c c|c c c c} \hline \hline \multirow{2}{*}{**Fold**} & \multicolumn{2}{c}{**Standalone**} & \multicolumn{2}{c}{**Standalone**} & \multirow{2}{*}{**Voting**} & \multirow{2}{*}{**Bidding**} & \multirow{2}{*}{**Scoring**} & \multirow{2}{*}{**Stacking**} \\  & **Average** & **Best (Baseline)** & & & & \\ \hline \#1 & 0.9458 & 0.9519 & 0.9584 & 0.9608 & **0.9718** & **0.9718** \\ \#2 & 0.9252 & 0.9538 & 0.9495 & 0.9589 & 0.9677 & **0.9700** \\ \#3 & 0.9280 & 0.9550 & 0.9490 & 0.9597 & 0.9668 & **0.9715** \\ \#4 & 0.9459 &  
The results presented in Tables 3-5 are compiled and visualized as a heatmap in Figure 5. The upper section of the figure depicts a comparison of all standalone taggers and unidirectionally built composite methods, while the lower section does the same but for bidirectionally built composite ones. The relative improvements visualized in the heatmap were also quantified as percentages of the error reduction using the formula  
\[\text{Error Reduction}=\frac{a_{1}-a_{0}}{1-a_{0}} \tag{3}\]  
where \(a_{0}\) is the initial accuracy and \(a_{1}\) is the supposedly improved one. The obtained results are numerically presented as in Table 6, where the left side shows the error reduction achieved using the unidirectionally-built composite methods, and the right side shows the same for the bidirectionally-built methods. The comparison of the results achieved using unidirectionally-built composite methods (Table 4) and bidirectionally-built composite methods (Table 5) was recompiled to \begin{table}
\begin{tabular}{c|c c c c|c c c} \hline \hline
**Fold** & **Voting** & **Bidding** & **Scoring** & **Stacked** & **Voting** & **Bidding** & **Scoring** & **Stacked** \\ \hline \#1 & \(13.51\%\) & \(18.50\%\) & \(41.37\%\) & \(41.37\%\) & \(16.27\%\) & \(40.13\%\) & \(\mathbf{47.07\%}\) & \(\mathbf{47.07\%}\) \\ \#2 & \(-9.31\%\) & \(11.04\%\) & \(30.09\%\) & \(35.06\%\) & \(-0.43\%\) & \(34.42\%\) & \(44.16\%\) & \(\mathbf{46.32\%}\) \\ \#3 & \(-13.33\%\) & \(10.44\%\) & \(26.22\%\) & \(36.67\%\) & \(2.00\%\) & \(38.00\%\) & \(\mathbf{45.56\%}\) & \(45.33\%\) \\ \#4 & \(-11.94\%\) & \(9.23\%\) & \(35.81\%\) & \(37.16\%\) & \(9.68\%\) & \(37.16\%\) & \(42.57\%\) & \(\mathbf{43.92\%}\) \\ \#5 & \(14.35\%\) & \(14.13\%\) & \(28.70\%\) & \(37.09\%\) & \(22.96\%\) & \(42.83\%\) & \(41.72\%\) & \(\mathbf{47.46\%}\) \\ \hline average & \(-1.34\%\) & \(12.67\%\) & \(32.44\%\) & \(37.47\%\) & \(10.87\%\) & \(39.04\%\) & \(44.72\%\) & \(\mathbf{46.51\%}\) \\ minimum & \(-13.33\%\) & \(9.23\%\) & \(26.22\%\) & \(35.06\%\) & \(2.93\%\) & \(36.61\%\) & \(44.77\%\) & \(\mathbf{47.91\%}\) \\ maximum & \(14.35\%\) & \(18.50\%\) & \(41.37\%\) & \(41.37\%\) & \(21.40\%\) & \(41.67\%\) & \(45.05\%\) & \(\mathbf{46.40\%}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Relative error reduction achieved using the unidirectionally based composite methods (left) and bidirectionally built methods (right) for each of the five outer folds (upper) and the compiled metrics for each method (lower). Greatest improvements over the baseline are shown in bold. Figure 5: Heatmap depicting differences in achieved \(f_{1}\)-scores for all standalone taggers and unidirectionally built composite ones (upper) and bidirectionally built ones (lower). Yellow indicates the average \(f_{1}\)-scores, red (left-side) indicates the relative decrease, and green (right-side) indicates the relative increase in the score. indicate their mutual differences and the results are displayed in Table 7. The table shows relative \(f_{1}\) score improvements achieved using the bidirectional architecture over the nidirectional one (upper section) and the relative average, minimum, and maximum values and the stability improvement (lower section). Since the ambiguous words (ones that can be annotated with several different tags) are a common issue in POS-tagging, we analyzed a few well known difficult cases for Serbian to procure how different taggers resolved them.