A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective.

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time course of the intensity function of a point process (e.g., exponentially decreasing or increasing with the time since the most recent event). However, such an assumption can restrict the expressive power of the model. We herein propose a novel RNN based model in which the time course of the intensity function is represented in a general manner. In our approach, we first model the integral of the intensity function using a feedforward neural network and then obtain the intensity function as its derivative. This approach enables us to both obtain a flexible model of the intensity function and exactly evaluate the log-likelihood function, which contains the integral of the intensity function, without any numerical approximations. Our model achieves competitive or superior performances compared to the previous state-of-the-art methods for both synthetic and real datasets.

Modeling event sequences of multiple event types with marked temporal point processes (MTPPs) provides a principled way to uncover governing dynamical rules and predict future events. Current neural network approaches to MTPP inference rely on training separate, specialized models for each target system. We pursue a radically different approach: drawing on amortized inference and in-context learning, we pretrain a deep neural network to infer, in-context, the conditional intensity functions of event histories from a context defined by sets of event sequences. Pretraining is performed on a large synthetic dataset of MTPPs sampled from a broad distribution of Hawkes processes. Once pretrained, our Foundation Inference Model for Point Processes (FIM-PP) can estimate MTPPs from real-world data without any additional training, or be rapidly finetuned to target systems. Experiments show that this amortized approach matches the performance of specialized models on next-event prediction across common benchmark datasets. Our pretrained model, repository and tutorials will soon be available online

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.

Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with the causal generative process of the network that occurs in time. Hence, exploiting the temporal aspect of networks has been the focus of many recent studies. In this context, we propose a new framework for generative models of continuous-time temporal networks. We assume that the activation of the edges in a temporal network is driven by a specified temporal point process. This approach allows to directly model the waiting time between events while incorporating time-varying history-based features as covariates in the predictions. Coupled with a thinning algorithm designed for the simulation of point processes, SimHawNet enables simulation of the evolution of temporal networks in continuous time. Finally, we introduce a comprehensive evaluation framework to assess the performance of such an approach, in which we demonstrate that SimHawNet successfully simulates the evolution of networks with very different generative processes and achieves performance comparable to the state of the art, while being significantly faster.

Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they are emerging as a promising choice for capturing the patterns in asynchronous sequences, in the context of temporal point process. In this paper, we first review recent research emphasis and difficulties in modeling asynchronous event sequences with deep temporal point process, which can be concluded into four fields: encoding of history sequence, formulation of conditional intensity function, relational discovery of events and learning approaches for optimization. We introduce most of recently proposed models by dismantling them into the four parts, and conduct experiments by remodularizing the first three parts with the same learning strategy for a fair empirical evaluation. Besides, we extend the history encoders and conditional intensity function family, and propose a Granger causality discovery framework for exploiting the relations among multi-types of events. Because the Granger causality can be represented by the Granger causality graph, discrete graph structure learning in the framework of Variational Inference is employed to reveal latent structures of the graph. Further experiments show that the proposed framework with latent graph discovery can both capture the relations and achieve an improved fitting and predicting performance.

Asynchronous event sequence clustering aims to group similar event sequences in an unsupervised manner. Mixture models of temporal point processes have been proposed to solve this problem, but they often suffer from overfitting, leading to excessive cluster generation with a lack of diversity. To overcome these limitations, we propose a Bayesian mixture model of Temporal Point Processes with Determinantal Point Process prior (TP$^2$DP$^2$) and accordingly an efficient posterior inference algorithm based on conditional Gibbs sampling. Our work provides a flexible learning framework for event sequence clustering, enabling automatic identification of the potential number of clusters and accurate grouping of sequences with similar features. It is applicable to a wide range of parametric temporal point processes, including neural network-based models. Experimental results on both synthetic and real-world data suggest that our framework could produce moderately fewer yet more diverse mixture components, and achieve outstanding results across multiple evaluation metrics.

In my opinion this paper is quite good, although I do not consider myself an expert on point processes, which should be taken into account when reading this review. I consider it in the top 50% of NIPS papers as a lower bound, admitting that I do not know enough to evaluated it further. I have asked the committee to ensure that at least one person who can judge the proofs sufficiently be assigned to this paper and they promised me this would be the case. I do hope if is published as I would like to try using it. Overall I think the main issue with this paper is that it would more comfortably fit in about 20 pages.

Modeling the dynamics of interacting entities using an evolving graph is an essential problem in fields such as financial networks and e-commerce. Traditional approaches focus primarily on pairwise interactions, limiting their ability to capture the complexity of real-world interactions involving multiple entities and their intricate relationship structures. This work addresses the problem of forecasting higher-order interaction events in multi-relational recursive hypergraphs. This is done using a dynamic graph representation learning framework that can capture complex relationships involving multiple entities. The proposed model, \textit{Relational Recursive Hyperedge Temporal Point Process} (RRHyperTPP) uses an encoder that learns a dynamic node representation based on the historical interaction patterns and then a hyperedge link prediction based decoder to model the event's occurrence. These learned representations are then used for downstream tasks involving forecasting the type and time of interactions. The main challenge in learning from hyperedge events is that the number of possible hyperedges grows exponentially with the number of nodes in the network. This will make the computation of negative log-likelihood of the temporal point process expensive, as the calculation of survival function requires a summation over all possible hyperedges. In our work, we use noise contrastive estimation to learn the parameters of our model, and we have experimentally shown that our models perform better than previous state-of-the-art methods for interaction forecasting.

We introduce the Piecewise-Constant Conditional Intensity Model, a model for learning temporal dependencies in event streams. We describe a closed-form Bayesian approach to learning these models, and describe an importance sampling algorithm for forecasting future events using these models, using a proposal distribution based on Poisson superposition. We then use synthetic data, supercomputer event logs, and web search query logs to illustrate that our learning algorithm can efficiently learn nonlinear temporal dependencies, and that our importance sampling algorithm can effectively forecast future events.