# An Inference Framework of Markov Logic Network for Link Prediction in Heterogeneous Networks
## 5 Experiments
### Experimental Results
The total execution time (TT), time for the E-step (ToE), and time for the M-step (ToM) are illustrated in Figure 4. It is noteworthy that the execution times of MLN and NMLN are not included due to their significantly longer durations compared to the listed methods. Our observations reveal the following:  
* On WN18 RR and FB15k-237 datasets, each containing over 10,000 entities, our method demonstrates the shortest processing time and surpasses the second-fastest model by an average of 42.37%. * When compared to pgat, RNNlogic, ExpressGNN, and PlogicNet on FB15k-237, our method reduces the total execution time (TT) by 40%, 56.82%, 63.3%, and 69.7%, respectively. On WN18 RR, our method outperforms pgat, RNNlogic, ExpressGNN, and PlogicNet by 19.09%, 42.86%, 49.14%, and 55.5%, respectively. * In terms of the E-step (ToE) and M-step (ToM), our method achieves average improvements of 57.85% and 21.15% on WN18 RR, and 71.96% and 37.41% on FB15k-237, respectively. These results illustrated in Figure 4 denote that our method demonstrates efficiency advancements on TT, ToE, and ToM, on the datasets with more than 10,000 entities. Moreover, to assess efficiency across datasets of different sizes, we compared the total execution time (TT) on UMLS, Kinship, Aminer-10000, Aminer-5000, Aminer-2000, and Aminer-1000, each comprising fewer than 10,000 entities, as depicted in Figure 5a. Furthermore, Figure 5b presents the TT, time for the E-step (ToE), and time for the M-step (ToM) of our method, showcasing the execution durations of these steps across various dataset sizes. Our analysis indicates the following:  
* As depicted in Figure 5a, our method exhibits the shortest total execution time among the datasets containing fewer than 10,000 entities, surpassing RNNlogic, Pgat, and PlogicNet. On average, our model consumes 33.2% less time than the second-fastest model in each dataset. * As illustrated in Figure 5b, the execution time for the M-step (ToM) in our method averages 26% more than that for the E-step (ToE) across different datasets. Furthermore, the total time (TT) of our model demonstrates exponential growth with increasing data size, whereas both ToE and ToM exhibit nearly linear growth. **Impacts of parameters. ** We assessed the influence of experimental variables on the efficacy of LP by examining the accuracy of different methods while altering the number of formulas on Aminer-1000, FB15k-237, and Kinship datasets with more than 3 formulas, as detailed in Table 9. Our analysis indicates that:  
Figure 4: TT, Toe, and ToM on datasets with more than 10,000 entities. (**a**) FB15k-237; (**b**) WN18 RR. * Our method attains average accuracies of 81.03%, 91.54%, and 44.39% on Aminer-10000, FB15k-237, and Kinship, respectively, surpassing the second-best competitors by 3.75%, 2.87%, and 11.55% on average. This underscores the robustness of our approach. * Accuracy shows a slight increment with an increase in logical formulas, suggesting that more formulas lead to improved accuracy. Conversely, a higher number of formulas results in a substantially larger grounded MLN structure, introducing more unlabeled nodes in MLN that could potentially impact accuracy negatively. Notably, as depicted in Table 9, the accuracy on PlogicNet decreases by an average of 1.34% with the increase in formulas. **Ablation study. ** We conducted ablation experiments on the distinct contributions of each component in our proposed framework, the results of which are shown in Table 10. The base MLN with SRL establishes a foundation but shows limitations on larger, complex datasets like FB15k and WN18 RR. The VEM-GCN integration substantially enhances performance with a 7-12% across all datasets. Substructure condition (SC) presents an intriguing efficiency-accuracy trade-off. While moderately impacting accuracy with a reduction of only 1-2%, SC substantially enhances computational efficiency, delivering processing speeds up to 3.5x faster on larger datasets.