# From Scores to Predictions in Multi-Label Classification: Neural Thresholding Strategies
## 5 Experiments and Results
### Real Datasets
#### 5.2.3 Quantitative Results  
In Tables 2 and 3, we present the results of the four described score datasets on held-out test splits. In almost all cases, ThresNet\({}_{CSS}\) performed best between single models and ensembles. According to \(F^{avg}\), the method turned out to be better than the best traditional method in all cases, with improvements ranging from 0.01 (EURLex4K\({}^{\text{LEML}}\)) to 0.09 (SimpleWiki2K\({}^{\text{LEML}}\)). Interestingly, sometimes the hybrid ThresNet\({}_{CSS}\) with CSS was profitable, although ThresNet\({}_{CSS}\) used CSS thresholds internally. Higher \(F^{avg}\) achieved by neural thresholding can be attributed to much better \(F^{mi}\). Neural nets naturally optimize for \(F^{mi}\) because training is performed example by example, and the optimization is conducted for all labels simultaneously; each output unit participates in the binary cross entropy. On the other hand, the CSS-cut strategy fits each threshold per label separately, so it optimizes a \(F^{ma}\) metric. In fact, with the exception of SimpleWiki2K\({}^{\text{LEML}}\), CSS is much better than our neural methods (excluding hybrids) in terms of this metric. The addition of CSS priors in ThresNet\({}_{CSS}\) improves \(F^{ma}\) considerably, but it still was not enough to reach CSS in this metric. We speculate that the main reason \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Thresholding Method**} & \multicolumn{3}{c}{**\(k\)-NN Scores**} & \multicolumn{3}{c}{**LEML Scores**} \\ \cline{2-7}  & \(F^{mi}\) & \(F^{ma}\) & \(F^{\text{avg}}\) & \(F^{mi}\) & \(F^{ma}\) & \(F^{avg}\) \\ \hline CSS (single) & 0.434 & 0.299 & 0.367 & 0.429 & 0.168 & 0.299 \\ ThresNet (single) & 0.556 & 0.222 & 0.389 & 0.602 & 0.169 & 0.386 \\ ThresNet\({}_{CSS}\) (single) & **0.592** & 0.235 & **0.413** & **0.603** & 0.174 & **0.389** \\ CSS+ThresNet (single) & 0.444 & 0.297 & 0.371 & 0.470 & 0.189 & 0.329 \\ CSS+ThresNet\({}_{CSS}\) (single) & 0.449 & **0.304** & 0.377 & 0.472 & **0.193** & 0.332 \\ \hline CSS (ensemble) & 0.442 & 0.308 & 0.375 & 0.434 & 0.177 & 0.306 \\ ThresNet (ensemble) & 0.602 & 0.216 & 0.409 & **0.622** & 0.165 & 0.394 \\ ThresNet\({}_{CSS}\) (ensemble) & **0.608** & 0.236 & **0.422** & **0.622** & 0.169 & **0.396** \\ CSS+ThresNet (ensemble) & 0.459 & 0.314 & 0.387 & 0.500 & 0.210 & 0.355 \\ CSS+ThresNet\({}_{CSS}\) (ensemble) & 0.467 & **0.320** & 0.393 & 0.502 & **0.213** & 0.358 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thresholding results on the SimpleWiki2K test set and scores given by \(k\)-NN and LEML scores. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Thresholding Method**} & \multicolumn{3}{c}{**\(k\)-NN Scores**} & \multicolumn{3}{c}{**LEML Scores**} \\ \cline{2-7}  & \(F^{mi}\) & \(F^{ma}\) & \(F^{\text{avg}}\) & \(F^{mi}\) & \(F^{ma}\) & \(F^{avg}\) \\ \hline CSS (single) & 0.344 & **0.211** & 0.278 & 0.425 & 0.166 & 0.295 \\ ThresNet (single) & 0.433 & 0.137 & 0.285 & **0.469** & 0.141 & 0.305 \\ ThresNet\({}_{CSS}\) (single) & **0.441** & 0.182 & **0.311** & 0.467 & 0.142 & 0.305 \\ CSS+ThresNet (single) & 0.331 & 0.206 & 0.268 & 0.446 & 0.167 & 0.307 \\ CSS+ThresNet\({}_{CSS}\) (single) & 0.339 & 0.210 & 0.274 & 0.447 & **0.169** & **0.308** \\ \hline CSS (ensemble) & 0.356 & **0.219** & 0.287 & 0.428 & 0.166 & 0.297 \\ ThresNet (ensemble) & 0.464 & 0.144 & 0.304 & 0.467 & 0.130 & 0.299 \\ ThresNet\({}_{CSS}\) (ensemble) & **0.480** & 0.152 & **0.316** & **0.479** & 0.139 & 0.309 \\ CSS+ThresNet (ensemble) & 0.354 & 0.217 & 0.285 & 0.445 & 0.171 & 0.308 \\ CSS+ThresNet\({}_{CSS}\) (ensemble) & 0.353 & 0.215 & 0.284 & 0.450 & **0.173** & **0.311** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thresholding results on the EURLex4K test set and scores given by \(k\)-NN and LEML scores. for the fact that a better \(F^{mi}\) does not entail a better \(F^{ma}\) is that output neurons responsible for predictions for the smallest classes received few positive examples to correctly set their weights.