Over the past two decades, there has been a tremendous increase in the growth
of representation learning methods for graphs, with numerous applications
across various fields, including bioinformatics, chemistry, and the social
sciences. However, current dynamic network approaches focus on discrete-time
networks or treat links in continuous-time networks as instantaneous events.
Therefore, these approaches have limitations in capturing the persistence or
absence of links that continuously emerge and disappear over time for
particular durations. To address this, we propose a novel stochastic process
relying on survival functions to model the durations of links and their
absences over time. This forms a generic new likelihood specification
explicitly accounting for intermittent edge-persistent networks, namely GraSSP:
Graph Representation with Sequential Survival Process. We apply the developed
framework to a recent continuous time dynamic latent distance model
characterizing network dynamics in terms of a sequence of piecewise linear
movements of nodes in latent space. We quantitatively assess the developed
framework in various downstream tasks, such as link prediction and network
completion, demonstrating that the developed modeling framework accounting for
link persistence and absence well tracks the intrinsic trajectories of nodes in
a latent space and captures the underlying characteristics of evolving network
structure.

在过去的二十年中，图形的表示学习方法有了巨大的增长，具有多个应用领域，包括生物信息学、化学和社会科学。然而，目前的动态网络方法侧重于离散时间网络，或者将连续时间网络中的链接视为瞬时事件。为了解决这个问题，我们提出了一种依赖于生存函数的新型随机过程，用于建模链接的持续时间和它们在一段时间内的缺失。我们将这一方法应用于最近的连续时间动态潜在距离模型，并在链接预测和网络完成等各种下游任务中进行量化评估，证明这一开发的建模框架很好地追踪了潜在空间中节点的内在轨迹，并捕捉了演化网络结构的潜在特征。

连续时间图表示与序贯生存过程

Continuous-time Graph Representation with Sequential Survival Process

Representation learning methods have revolutionized machine learning on
networks by converting discrete network structures into continuous domains.
However, dynamic networks that evolve over time pose new challenges. To address
this, dynamic representation learning methods have gained attention, offering
benefits like reduced learning time and improved accuracy by utilizing temporal
information.
T-batching is a valuable technique for training dynamic network models that
reduces training time while preserving vital conditions for accurate modeling.
However, we have identified a limitation in the training loss function used
with t-batching. Through mathematical analysis, we propose two alternative loss
functions that overcome these issues, resulting in enhanced training
performance.
We extensively evaluate the proposed loss functions on synthetic and
real-world dynamic networks. The results consistently demonstrate superior
performance compared to the original loss function. Notably, in a real-world
network characterized by diverse user interaction histories, the proposed loss
functions achieved more than 26.9% enhancement in Mean Reciprocal Rank (MRR)
and more than 11.8% improvement in Recall@10. These findings underscore the
efficacy of the proposed loss functions in dynamic network modeling.

表示学习方法在将离散网络结构转化为连续领域方面为机器学习提供了革命性进展，但是动态网络在时间上的演变带来了新的挑战。我们通过数学分析提出了两种新的损失函数来克服 t-batching 中训练损失函数的局限性，并在合成和真实动态网络上进行了广泛评估，结果一致显示出比原始损失函数更优越的性能，尤其在具有多样的用户交互历史的真实网络中，所提出的损失函数在 Mean Reciprocal Rank（MRR）上实现了超过 26.9% 的增强和 Recall@10 上的超过 11.8% 的改善，这些发现凸显了动态网络建模中所提出的损失函数的功效。