Hierarchical Contrastive Learning for Temporal Point Processes

As an essential sequential model, the temporal point process (TPP) plays a central role in real-world sequence modelling and analysis, whose learning is often based on the maximum likelihood estimation (MLE). However, due to imperfect observations, such as incomplete and sparse sequences that are common in practice, the MLE of TPP models often suffers from overfitting and leads to unsatisfactory generalization power. In this work, we develop a novel hierarchical contrastive (HCL) learning method for temporal point processes, which provides a new regularizer of MLE. In principle, our HCL considers the noise contrastive estimation (NCE) problem at the event-level and that at the sequencelevel jointly. Given a sequence, the event-level NCE maximizes the probability of each observed event given its history while penalizing the conditional probabilities of the unobserved events. At the same time, we generate positive and negative event sequences from the observed sequence and maximize the discrepancy between their likelihoods through the sequence-level NCE. Instead of using time-consuming simulation methods, we generate the positive and negative sequences via a simple but efficient model-guided thinning process. Experimental results show that the MLE method assisted by the HCL regularizer outperforms classic MLE and other contrastive learning methods in learning various TPP models consistently. The code is available at https://github. com/qingmeiwangdaily/HCL TPP.