# Exploring the Performance of Continuous-Time Dynamic Link Prediction Algorithms
## 1 Introduction  
Many real-world phenomena such as computers networks [1], epidemics [2], neural networks [3], email exchanges [4], and face-to-face interactions [4, 5] can be modeled as a set of objects interacting through time. These types of data are commonly represented as a dynamic graph [6], where nodes represent the objects while edges represent pairs of objects that interact through time. While initial attempts at capturing the temporal evolution of networks typically aggregated the interactions into a sequence of static graphs, recent efforts incorporate time continuously, avoiding the loss of some fine-grained temporal information during data preprocessing [6, 7]. The resulting types of data are commonly referred to as Continuous-Time Dynamic Graphs (CTDGs) [8]. Modeling and forecasting CTDGs have recently become very active fields of research, as suggested by recent surveys [9, 10]. A crucial task of interest is Dynamic Link Prediction (DLP), where the goal is to predict future links from a history of observed ones. This task has gained considerable attention, as seen from recent benchmarks [11], and finds notable applications in recommender systems, influence detection, routing in networks or disease prediction [12, 13], to name a few. Creating a standardized evaluation for Dynamic Link Prediction (DLP) algorithms poses significant challenges [8]. Firstly, the benchmark datasets available vary widely in nature, leading to different domain-specific DLP tasks. Predicting which pair of students will have a face-to-face interaction in the HighSchool dataset at a given time is, for instance, very different from predicting which item a given user will interact with in the Wikipedia dataset. Secondly, the evaluation pipelines differ among methods. This often results innear-perfect performance metrics and contributes to a bias where each paper tends to favor its own proposed approach. Lastly, typical metrics for DLP will compare the score of the actual interactions occurring in the dynamic graph with the scores of interactions that did not happen, obtained through random negative sampling (NS) [14]. As underlined in [8], the procedure used to generate these negative events can have a dramatic impact on DLP performance measures, to the point that some sophisticated methods can often be outperformed by parameter-free heuristics. As a result, there is a growing awareness that Dynamic Link Prediction performance measures not only depend on the model quality and the challenging nature of the data, but crucially also on the strategy for sampling negative events. Notably, a suggestion proposed by [PERSON] et al. [8] was to generate more challenging negative samples by examining which edges were previously seen or not at test time. These conclusions align with the guidelines proposed by [PERSON] et al. [15], who suggest splitting the DLP task into two tasks: predicting previously observed links and predicting previously unobserved links, with each of these tasks coming with their own specific metrics. This same work attributes these challenges to the fact that, while conventional machine learning tasks target independent and identically distributed (iid) data, _events_, _nodes_, and _node pairs_ in a (dynamic) graph do not satisfy this property. As a consequence, the prediction performance is likely to exhibit substantial variations depending on the node, edge, or time interval considered. Despite this growing awareness, central aspects of the DLP task remain ambiguous to this day. Notably, there is a lack of tools for understanding the domain-dependent effect of splitting a history of interaction into a train history and a test history based on a cutoff time. Yet, such an understanding is crucial for designing relevant NS strategies for evaluation. Furthermore, the time evolution of prediction performance tends to be disregarded, despite its significant relevance in real-world applications. **Contributions**.