# Enhanced Knowledge Graph Embedding by Jointly Learning Soft Rules and Facts
## 5 Experiment
### Results
#### 5.3.2 Influence of the Confidence Threshold  
Here, we investigate how the confidence threshold influenced the performance of our method. We conducted the link prediction experiments on FB15K, where the hyper-parameters were fixed to the optimal configurations and the confidence thresholds were varied from 0.5 to 1.0 with an increment of 0.05. Figure 3 reports the results of MRR and HITS@1 achieved by SoLE with various thresholds. From the results, we can see that these two metrics had the same trend, and they both achieved the best performance when the threshold was 0.8. Thresholds higher than 0.8 will have a smaller number of rules, which can be extracted in the grounding generation stage, while ones lower than that might introduce too many less credible rules. Therefore, after the threshold exceeded 0.8, the performance decreased when the threshold grew, and after it was lower than that, the performance also decreased when the threshold decreased. Based on this observation, we assigned the confidence threshold to 0.8 in SoLE and obtained the best performance.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \(n_{g}\) & MRR & HITS@1 & HITS@3 & HITS@10 \\ \hline SoLE\_OTI & 115,553 & 0.800 & 0.763 & 0.820 & 0.867 \\ SoLE & 126,423 & 0.801 & 0.764 & 0.821 & 0.867 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Link prediction results achieved by SoLE with One Time Inference (SoLE_OTI) and forward chaining (SoLE) on FB15K; \(n_{g}\) denotes the number of groundings derived in the grounding generation stage.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**FB15K**} & \multicolumn{4}{c}{**DB100K**} \\ \cline{2-9}
**Method** & **MRR** & **HITS@1** & **HITS@3** & **HITS@10** & **MRR** & **HITS@1** & **HITS@3** & **HITS@10** \\ \hline TransE [17] & 0.380 & 0.231 & 0.472 & 0.641 & 0.111 & 0.016 & 0.164 & 0.270 \\ DisMult [33] & 0.654 & 0.546 & 0.733 & 0.824 & 0.233 & 0.115 & 0.301 & **0.448** \\ ANALOGY [34] & 0.725 & 0.646 & 0.785 & 0.854 & 0.252 & 0.143 & 0.323 & 0.427 \\ CompIEx [18] & 0.718 & 0.645 & 0.768 & 0.840 & 0.289 & 0.214 & 0.324 & 0.427 \\ ConvE [19] & 0.745 & 0.670 & 0.801 & 0.873 & - & - & - & - \\ R-GCN+ [35] & 0.696 & 0.601 & 0.760 & 0.842 & - & - & - & - \\ \hline CompIEx\({}^{R}\)[12] & - & - & - & - & 0.253 & 0.167 & 0.294 & 0.420 \\ RUGE [14] & 0.768 & 0.703 & 0.815 & 0.865 & 0.246 & 0.129 & 0.325 & 0.433 \\ ComplEx-NNE+AER [13] & 0.803 & 0.761 & **0.831** & **0.874** & **0.306** & 0.244 & **0.334** & 0.418 \\ pLogicNet [27] & 0.776 & 0.706 & 0.817 & 0.885 & - & - & - & - \\ IterE [26] & 0.628 * & 0.551 * & 0.673 * & 0.771 * & - & - & - & - \\ \hline SoLE & 0.801 & 0.764 & 0.821 & 0.867 & **0.306** & 0.248 & 0.328 & 0.418 \\  & 0.668 * & 0.604 * & 0.699 * & 0.794 * & & & \\ SoLE-NNE & **0.805** & **0.769** & 0.825 & 0.870 & **0.306** & **0.249** & 0.326 & 0.414 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Link prediction results with Mean Reciprocal Rank (MRR) and HITS@Non the test sets of FB15K and DB100K. Boldface scores are the best results, and underlined ones are the second best. “-” indicates the missing scores not reported in the literature, and “*” indicates the results are evaluated on the sparse test sets of FB15K, i.e., the test sets of FB15K-sparse.