continuous-time nmf

This work addresses a key limitation of traditional non-negative matrix factorization (NMF) when applied to continuous-time event data: the need for binning or smoothing, which often obscures individual heterogeneity and fine-grained temporal dynamics. To overcome this, the authors propose EventNMF, the first continuous-time NMF model that operates directly on event sequences without preprocessing. EventNMF models events as a Poisson process whose intensity function admits a low-rank non-negative decomposition, leveraging non-negative B-spline bases to extract interpretable, shared temporal patterns across entities. Theoretical analysis reveals that conventional binning corresponds to a zeroth-order B-spline special case and elucidates the inherent bias–variance trade-off. Experiments on both synthetic and real-world datasets demonstrate that EventNMF consistently outperforms existing approaches while offering mathematical rigor, implementation simplicity, and computational efficiency.

This paper addresses the limitation of conventional temporal point processes in capturing complex historical dependencies—such as periodicity, burstiness, and inhibition—by proposing a novel point process model with an explicit memory mechanism. Methodologically, it introduces, for the first time, a locally mixed first-order hazard function into conditional intensity modeling; establishes a dependency update process framework enabling both stationary marginal distribution design and duration-based clustering extensions; and integrates Bayesian inference, mixture modeling of conditional inter-event time densities, and higher-order Markov dependency structures. Theoretically, the model’s properties are rigorously analyzed. Empirical evaluations on synthetic and real-world datasets demonstrate significant improvements in modeling accuracy and predictive performance across diverse memory patterns. Notably, the model excels in extended scenarios such as clustered point processes, underscoring its flexibility and practical utility.

Traditional machine learning approaches for scientific event sequence analysis require task-specific modeling and incur high training costs. Method: This paper introduces the first general-purpose foundation model for temporal point processes (TPPs), built upon a deep neural architecture that integrates context-aware mechanisms with principled TPP theory, trained via large-scale synthetic data-driven self-supervised pretraining. Contribution/Results: The model achieves unified cross-domain representation of event patterns, enabling zero-shot inference and rapid few-shot fine-tuning. Experiments across domains—including medicine and seismology—demonstrate its plug-and-play usability without task-specific training while maintaining competitive performance; subsequent fine-tuning yields significant accuracy gains. By eliminating the need for per-task architecture design and extensive retraining, the model substantially lowers modeling barriers and computational overhead, thereby accelerating scientific discovery.

To address computational inefficiency and limited representational capacity arising from explicit intensity function modeling in high-dimensional marked temporal point processes, this paper proposes an intensity-free implicit conditional generative framework. Methodologically, we pioneer the integration of implicit generative modeling into marked point processes, designing an end-to-end differentiable architecture that jointly encodes event timestamps, types, and high-dimensional marks (e.g., text, images), leveraging conditional GANs and sequence encoders for history-driven, high-fidelity future event generation. Our core contribution lies in eliminating reliance on parametric intensity functions, thereby significantly enhancing dynamic modeling capability and sampling efficiency. Extensive experiments on multiple real-world high-dimensional datasets demonstrate that our approach outperforms state-of-the-art methods in both event generation quality and prediction accuracy, while accelerating training by over 3×.

Long-term forecasting of irregularly spaced temporal event sequences remains challenging for existing autoregressive models, which suffer from error accumulation and myopic prediction horizons. To address this, we propose EventFlow, the first non-autoregressive generative model for continuous-time event modeling that introduces flow matching to directly learn the joint distribution over event times—enabling likelihood-free, end-to-end joint modeling. EventFlow parameterizes the velocity field via neural ordinary differential equations (neural ODEs), integrating event-time embeddings and temporal encodings to support efficient sampling, stable training, and both unconditional and conditional generation. On multiple standard benchmarks, EventFlow achieves predictive accuracy competitive with or superior to state-of-the-art autoregressive methods (e.g., THP, DyRep), while accelerating sampling by 3–5× and demonstrating enhanced training robustness.

This work proposes a nonparametric spatiotemporal point process model based on Gaussian processes to overcome the limitations of traditional approaches, which often rely on restrictive parametric assumptions or lack interpretability in capturing complex event dependencies. The model employs a separable kernel and a structured grid to separately represent the background intensity and the triggering influence kernel, thereby achieving both flexibility and interpretability. To enhance scalability, the method leverages a Kronecker-structured covariance matrix and tensor-product Gauss–Legendre quadrature, enabling efficient handling of large-scale spatiotemporal event data. Experimental results demonstrate that the proposed approach significantly outperforms existing models across multiple real-world datasets, offering superior predictive accuracy and computational efficiency.

This work proposes a Bayesian nonparametric clustering method for replicated marked Poisson point process data, jointly inferring the latent cluster structure, the number of clusters, and the intensity surface associated with continuous marks. Built upon a Dirichlet process mixture model, the approach employs a squared link function to model the intensity surface and leverages variational Bayesian inference for efficient learning. To address sign ambiguity and nodal line issues inherent in the squared link, the method introduces a constrained Laplace approximation that reformulates the non-conjugate basis coefficient updates as a constrained optimization problem, thereby providing theoretical guarantees for mode-finding. Experimental results demonstrate that the proposed model achieves superior performance in clustering accuracy, intensity estimation, and computational efficiency on both synthetic and real-world datasets.

This work addresses key limitations of existing neural temporal point process models, which often suffer from low training efficiency due to sequential event processing and difficulty in directly modeling smooth conditional intensity functions. The authors propose a novel approach that, for the first time, employs B-spline basis functions to directly parameterize the conditional intensity, with non-negative combination coefficients predicted by an arbitrary neural network. This formulation enables exact maximum likelihood estimation, supports highly efficient parallel training, and incorporates natural smoothness regularization through integration of second-order derivatives. Experimental results demonstrate that the proposed model significantly outperforms current baselines on both synthetic and real-world datasets, achieving simultaneous improvements in predictive accuracy and training efficiency.

This work addresses the challenge of predicting irregular event sequences by jointly modeling dependencies among discrete event types and continuous-time dynamics. To this end, the authors propose the NEXTPP framework, which employs self-attention to encode event tokens, neural ordinary differential equations (Neural ODEs) to model continuous latent state evolution, and cross-attention mechanisms to enable bidirectional interaction between the discrete and continuous components. This integrated approach drives the conditional intensity function of a neural Hawkes process and represents the first unified framework for coupling discrete event markers with continuous temporal dynamics. By doing so, NEXTPP overcomes key limitations of existing methods in jointly capturing asynchronous dependencies and temporal evolution. Extensive experiments on five real-world datasets demonstrate that NEXTPP consistently outperforms state-of-the-art models, achieving significant improvements in event prediction performance.

This work addresses the lack of reliable and reproducible comparisons among existing neural spatiotemporal point process (STPP) models, which stems from inconsistent preprocessing, coordinate normalization, data partitioning, and evaluation protocols. To remedy this, we propose SEAHORSE, a unified benchmarking framework that enables fair training, tuning, and evaluation of diverse neural STPP models through a standardized encode-evolve-decode architecture, likelihood computation in raw coordinates, and consistent evaluation protocols. We further introduce HawkesNest, a novel synthetic stress-test suite that systematically reveals the inductive biases of different models under complex event patterns. Experiments demonstrate that model performance is highly sensitive to the complexity of event dynamics: some methods degrade sharply while others remain robust, underscoring the critical value of our benchmark for analyzing model robustness.