Temporal Point Processes (TPPs) have been widely used for event sequence modeling, but they often struggle to incorporate rich textual event descriptions effectively. Conversely, while Large Language Models (LLMs) have been shown remarkable capabilities in processing textual data, they lack mechanisms for handling temporal dynamics. To bridge this gap, we introduce Language-TPP, a unified framework that integrates TPPs with LLMs for enhanced event sequence modeling. Language-TPP introduces a novel temporal encoding mechanism that converts continuous time intervals into specialized byte-tokens, enabling seamless integration with standard LLM architectures. This approach allows Language-TPP to achieve state-of-the-art performance across multiple TPP tasks, including event time prediction, type prediction, and intensity estimation, on five datasets. Additionally, we demonstrate that incorporating temporal information significantly improves the quality of generated event descriptions.

Temporal point processes (TPPs) are stochastic process models used to characterize event sequences occurring in continuous time. Traditional statistical TPPs have a long-standing history, with numerous models proposed and successfully applied across diverse domains. In recent years, advances in deep learning have spurred the development of neural TPPs, enabling greater flexibility and expressiveness in capturing complex temporal dynamics. The emergence of large language models (LLMs) has further sparked excitement, offering new possibilities for modeling and analyzing event sequences by leveraging their rich contextual understanding. This survey presents a comprehensive review of recent research on TPPs from three perspectives: Bayesian, deep learning, and LLM approaches. We begin with a review of the fundamental concepts of TPPs, followed by an in-depth discussion of model design and parameter estimation techniques in these three frameworks. We also revisit classic application areas of TPPs to highlight their practical relevance. Finally, we outline challenges and promising directions for future research.

In this study, we propose a novel deep spatio-temporal point process model, Deep Kernel Mixture Point Processes (DKMPP), that incorporates multimodal covariate information. DKMPP is an enhanced version of Deep Mixture Point Processes (DMPP), which uses a more flexible deep kernel to model complex relationships between events and covariate data, improving the model's expressiveness. To address the intractable training procedure of DKMPP due to the non-integrable deep kernel, we utilize an integration-free method based on score matching, and further improve efficiency by adopting a scalable denoising score matching method. Our experiments demonstrate that DKMPP and its corresponding score-based estimators outperform baseline models, showcasing the advantages of incorporating covariate information, utilizing a deep kernel, and employing score-based estimators.

Inhomogeneous Poisson process data defined on a continuous spatio-temporal domain has attracted immense attention recently in a wide variety of applications, including reliability analysis in manufacturing systems (Soleimani et al, 2017), event capture in sensing regions (Mutny and Krause, 2021), crime prediction in urban area (Shirota and Gelfand, 2017) and disease diagnosis based on medical records (Lasko, 2014). The reliable training of an inhomogeneous Poisson process model critically relies on a large amount of data to avoid overfitting, especially when modeling high-dimensional point processes. However, one challenge is that the available training data is routinely sparse or even partially missing in specific applications. Taking manufacturing failure and healthcare analysis as motivating examples: the modern manufacturing machines are reliable and sparsely fail; the individuals with healthy constitution will not visit hospital very often. The data missing problems also arise, e.g., the event location capture is intermittent for sensing systems because of weather or other related barriers.

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to three key hypotheses: parametric, linear and homogeneous. Recent work has attempted to address these limitations separately. This work aims to overcome all three assumptions simultaneously by proposing the flexible state-switching Hawkes processes: a flexible, nonlinear and nonhomogeneous variant where a state process is incorporated to interact with the point processes. The proposed model empowers Hawkes processes to be applied to time-varying systems. For inference, we utilize the latent variable augmentation technique to design two efficient Bayesian inference algorithms: Gibbs sampler and mean-field variational inference, with analytical iterative updates to estimate the posterior. In experiments, our model achieves superior performance compared to the state-of-the-art competitors.