# An Inference Framework of Markov Logic Network for Link Prediction in Heterogeneous Networks
## 5 Experiments
### Experimental Results
Our method achieves accuracies of 72.66%, 76.7%, 79.48%, and 81.75%, outperforming the second-highest model by an average of 3.65% on the Aminer datasets with 10,000, 5000, 2000, and 1000 individuals, respectively. Also, we conducted experiments on different missing link ratios to evaluate the robustness of our method. We randomly removed 10%, 30%, and 50% of the Kinship, UMLS, WN18 RR, and FB15k-237 datasets, respectively, and various sizes of Aminer. The accuracy comparisons are detailed in Table 8. Our findings suggest the following:  
* When 10% of the edges are removed, the performance of the model shows a slight overall decline, with more pronounced decreases in the sparse datasets such as WN18 RR and FB15k-237, reaching 5% and 6%, respectively. In other datasets, the performance degradation is relatively smaller, approximately 3.5-4%. * As the edge removal increases to 30%, performance degradation becomes more significant. The FB15k-237 dataset is most affected, with a 20% reduction, while WN18 RR shows a 15% decrease. Kinship, UMLS, and the Aminer series datasets experience reductions between 11 and 13%. * When 50% of edges are removed, all datasets undergo substantial performance deterioration. The FB15k-237 dataset remains the most severely impacted, with a 35% decrease; WN18 RR declines by 30%; Kinship decreases by 25%; UMLS exhibits the smallest relative reduction at 23%; and all Aminer series datasets uniformly experience a 26% decrease. * Overall, sparser graph structures (e.g., WN18 RR and FB15k-237) demonstrate higher sensitivity to edge removal, whereas denser relationship graphs (e.g., UMLS and Kinship) display better robustness. The Aminer series datasets, regardless of size, show similar patterns of performance degradation. The accuracy enhancements observed in multi-relational LP validate the efficacy and robustness of our method through the integration of the VEM-based inference framework. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Method** & **Kinship** & **UMLS** & **WN18 RR** & **FB15k-237** & **Aminer-10,000** & **Aminer-5000** & **Aminer-2000** & **Aminer-1000** \\ \hline SEAL & 81.14 & 77.5 & 9.55 & 9.93 & 63.21 & 85.17 & 76.91 & 70.66 \\ MF & 66.15 & 73.98 & - & 60.29 & 62.18 & 71.53 & 60.4 \\ ExpressGNN & 82.19 & 82.17 & - & 34.44 & 70.81 & 85.12 & 74.21 & 82.02 \\ MLN & 81.72 & 79.02 & - & - & - & 73.29 & 73.19 \\ PlogicNet & 79.17 & 76.79 & 29.18 & 19.74 & 61.39 & 68.91 & 71.59 & 72.91 \\ Pgat & 69.11 & 72.72 & 36.97 & 33.28 & 66.75 & 54.71 & 62.15 & 58.44 \\ RNNlogic & 50.06 & 63.55 & 41.91 & 23.19 & 52.13 & 61.28 & 62.51 & 65.01 \\ Ours & **89.46** & **82.11** & **39.4** & **41.41** & **74.91** & **85.19** & **82.04** & **81.66** \\ \hline \(p\)-value & 0.001 ** & 0.949 & 0.202 & 0.015 * & 0.044 * & 0.957 & 0.003 ** & 0.818 \\
95\% CI & [86.84, 92.08] & [78.93, 85.29] & [35.66, 43.14] & [37.52, 45.30] & [71.53, 78.29] & [82.46, 87.92] & [78.75, 85.33] & [78.34, 84.98] \\ \hline \hline \end{tabular} Note: The highest accuracy is indicated in bold. * \(p\) \(<\) 0.05, ** \(p\) \(<\) 0.01. CI = Confidence Interval. \(p\)-values show a comparison of our method against the best competitor.  
\end{table} 
Table 7: Accuracy with 2-type links and ratio 7/3 with statistical analysis. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{**Edge Removal**} \\ \cline{2-4}  & **10 (\%)** & **30 (\%)** & **50 (\%)** \\ \hline Kinship & 91.12 & 83.48 & 71.15 \\ UMLS & 84.28 & 77.72 & 67.24 \\ WN18 RR & 40.09 & 35.87 & 29.54 \\ FB15k-237 & 42.68 & 36.32 & 29.51 \\ Aminer-10000 & 79.99 & 72.49 & 61.66 \\ Aminer-5000 & 88.62 & 80.31 & 68.31 \\ Aminer-2000 & 83.82 & 75.97 & 64.62 \\ Aminer-1000 & 85.92 & 77.87 & 66.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Accuracy under various missing link ratios. **Efficiency. ** Efficiency evaluation of our method involved comparing its execution time with various MLN-based methods in multi-relational LP on the benchmarks WN18 RR, FB15k-237, and Aminer datasets.