# Exploring the Performance of Continuous-Time Dynamic Link Prediction Algorithms
## 6 Results
### How Do Performances of DLP Algorithms Vary over Different NS Strategies?  
In Figure 4a, we report the AUC scores against three edge-NS: historical edge, overlap edge, and inductive edge negative sampling strategies. Similarly, in Figure 4b, we report AUCs for three destination-NS: historical destination, overlap destination, and inductive destination, as defined in Section 4.2.  
Figure 4: Test AUC results obtained by comparing the scores of the positive events with the scores of the negative events, sampled using specific strategies. For DyRep and TGN, we retrained the models with 5 different seeds and report the mean and the standard deviation of the resulting AUCs. (**a**) Test AUC results employing various edge negative sampling strategies: historical edge (HE), overlap edge (OE), and inductive edge (IE). These strategies involve sampling negative edges (u’,v’) from sets corresponding to edges exclusively present during training, those present during both training and testing, and those exclusively present during testing, respectively. (**b**) Test AUC results employing various destination negative sampling strategies: historical destination (HD), overlap destination (OD), and inductive destination (ID). These strategies swap the destination node with one present during training, both training and testing, or exclusively during testing.  
In general, the AUC scores are higher when swapping only the destination node, as in Figure 4b. This makes sense when thinking that swapping the destination with random nodes may lead to edges that never happened overall, and thus to negative events that are very unlikely. The overlap edge and overlap destination seem to lead to lower scores in general. Indeed, these strategies yield events that hit a good trade-off between having enough memory about the associated nodes/edges to yield a high score, and being sufficiently novel so that the models do not know yet how to discriminate them from the positive event. In contrast, for historical edges and destination, the involved nodes and edges become relatively obsolete after a certain time, an effect which seems to be picked up by the models.  
Starting with the baselines, we note that EdgeBank and Preferential Attachment show very similar performances against historical and overlap edges, with EdgeBank performing worse than random (AUC < 0.5). This can be explained by remembering that, at test time, all the historical edges and overlap edges will have a score of 1. In contrast, the true event may have a score of 1 or 0 depending on whether the associated edges or nodes were previously observed. In that context, the false positive rate is greater than 0 only if the decision threshold is at least 1 (if it is below 1, all the negatives are predicted negative). When the decision threshold reaches the value 1, the number of false positives jumps to the number of negatives (all the negatives will be predicted as positives). In particular, the false positive rate will increase faster than the true positive rate, resulting in an AUC score lower than 0.5.  
These figures indicate that NS can be defined such that heuristic baselines outperform neural network-based methods. For instance, in the IE and ID settings, EdgeBank is better than TGN and DyRep on the Lastfm dataset. Moreover, on the Enron dataset, PA outperforms the three other methods in the OD setting, and slightly outperforms TGN in the ID and IE setting. This is counter-intuitive when remembering that PA does not retain any information about the edges active in the past, but only remembers which _node_ was active in the past.  
In general, TGN seems to yield a higher score than DyRep. This makes sense considering that DyRep has been shown to be a special case of TGN. However, there are some exceptions, notably in the overlap destination setting where DyRep is better on Lastfm, UCI, and Enron.