Marked event data captures events by recording their continuous-valued occurrence timestamps along with their corresponding discrete-valued types. They have appeared in various real-world scenarios such as social media, financial transactions, and healthcare records, and have been effectively modeled through Marked Temporal Point Process (MTPP) models. Recently, developing generative models for these MTPP models have seen rapid development due to their powerful generative capability and less restrictive functional forms. However, existing generative MTPP models are usually challenged in jointly modeling events' timestamps and types since: (1) mainstream methods design the generative mechanisms for timestamps only and do not include event types; (2) the complex interdependence between the timestamps and event types are overlooked. In this paper, we propose a novel generative MTPP model called BMTPP. Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach. Additionally, by adding joint noise to the marked temporal data space, BMTPP effectively captures and explicitly reveals the interdependence between timestamps and event types. Extensive experiments validate the superiority of our approach over other state-of-the-art models and its ability to effectively capture marked-temporal interdependence.
Retrieving temporal event sequences from textual descriptions is crucial for applications such as analyzing e-commerce behavior, monitoring social media activities, and tracking criminal incidents. To advance this task, we introduce TESRBench, a comprehensive benchmark for temporal event sequence retrieval (TESR) from textual descriptions. TESRBench includes diverse real-world datasets with synthesized and reviewed textual descriptions, providing a strong foundation for evaluating retrieval performance and addressing challenges in this domain. Building on this benchmark, we propose TPP-Embedding, a novel model for embedding and retrieving event sequences. The model leverages the TPP-LLM framework, integrating large language models (LLMs) with temporal point processes (TPPs) to encode both event texts and times. By pooling representations and applying a contrastive loss, it unifies temporal dynamics and event semantics in a shared embedding space, aligning sequence-level embeddings of event sequences and their descriptions. TPP-Embedding demonstrates superior performance over baseline models across TESRBench datasets, establishing it as a powerful solution for the temporal event sequence retrieval task.
Learning continuous-time point processes is essential to many discrete event forecasting tasks. However, integration poses a major challenge, particularly for spatiotemporal point processes (STPPs), as it involves calculating the likelihood through triple integrals over space and time. Existing methods for integrating STPP either assume a parametric form of the intensity function, which lacks flexibility; or approximating the intensity with Monte Carlo sampling, which introduces numerical errors. Recent work by Omi et al. [2019] proposes a dual network approach for efficient integration of flexible intensity function. However, their method only focuses on the 1D temporal point process. In this paper, we introduce a novel paradigm: AutoSTPP (Automatic Integration for Spatiotemporal Neural Point Processes) that extends the dual network approach to 3D STPP. While previous work provides a foundation, its direct extension overly restricts the intensity function and leads to computational challenges. In response, we introduce a decomposable parametrization for the integral network using ProdNet. This approach, leveraging the product of simplified univariate graphs, effectively sidesteps the computational complexities inherent in multivariate computational graphs. We prove the consistency of AutoSTPP and validate it on synthetic data and benchmark real-world datasets. AutoSTPP shows a significant advantage in recovering complex intensity functions from irregular spatiotemporal events, particularly when the intensity is sharply localized. Our code is open-source at https://github.com/Rose-STL-Lab/AutoSTPP.
A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given goal. Nonetheless, many of these tactics are semantically similar or lead to an execution error, wasting valuable resources in both cases. We address the problem of effectively pruning this search, using only synthetic data generated from previous proof attempts. We first demonstrate that it is possible to generate semantically aware tactic representations which capture the effect on the proving environment, likelihood of success and execution time. We then propose a novel filtering mechanism which leverages these representations to select semantically diverse and high quality tactics, using Determinantal Point Processes. Our approach, 3D-Prover, is designed to be general, and to augment any underlying tactic generator. We demonstrate the effectiveness of 3D-Prover on the miniF2F-valid and miniF2F-test benchmarks by augmenting the ReProver LLM. We show that our approach leads to an increase in the overall proof rate, as well as a significant improvement in the tactic success rate, execution time and diversity.
Classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes for decades. Recent advances have led to Neural Point Processes (NPPs), which promise greater flexibility and improvements over classical models. However, the currently-used benchmark dataset for NPPs does not represent an up-to-date challenge in the seismological community since it lacks a key earthquake sequence from the region and improperly splits training and testing data. Furthermore, initial earthquake forecast benchmarking lacks a comparison to state-of-the-art earthquake forecasting models typically used by the seismological community. To address these gaps, we introduce EarthquakeNPP: a collection of benchmark datasets to facilitate testing of NPPs on earthquake data, accompanied by a credible implementation of the ETAS model. The datasets cover a range of small to large target regions within California, dating from 1971 to 2021, and include different methodologies for dataset generation. In a benchmarking experiment, we compare three spatio-temporal NPPs against ETAS and find that none outperform ETAS in either spatial or temporal log-likelihood. These results indicate that current NPP implementations are not yet suitable for practical earthquake forecasting. However, EarthquakeNPP will serve as a platform for collaboration between the seismology and machine learning communities with the goal of improving earthquake predictability.
Continuous-time event sequences, in which events occur at irregular intervals, are ubiquitous across a wide range of industrial and scientific domains. The contemporary modeling paradigm is to treat such data as realizations of a temporal point process, and in machine learning it is common to model temporal point processes in an autoregressive fashion using a neural network. While autoregressive models are successful in predicting the time of a single subsequent event, their performance can be unsatisfactory in forecasting longer horizons due to cascading errors. We propose EventFlow, a non-autoregressive generative model for temporal point processes. Our model builds on the flow matching framework in order to directly learn joint distributions over event times, side-stepping the autoregressive process. EventFlow is likelihood-free, easy to implement and sample from, and either matches or surpasses the performance of state-of-the-art models in both unconditional and conditional generation tasks on a set of standard benchmarks
Temporal point processes (TPPs) are effective for modeling event occurrences over time, but they struggle with sparse and uncertain events in federated systems, where privacy is a major concern. To address this, we propose \textit{FedPP}, a Federated neural nonparametric Point Process model. FedPP integrates neural embeddings into Sigmoidal Gaussian Cox Processes (SGCPs) on the client side, which is a flexible and expressive class of TPPs, allowing it to generate highly flexible intensity functions that capture client-specific event dynamics and uncertainties while efficiently summarizing historical records. For global aggregation, FedPP introduces a divergence-based mechanism that communicates the distributions of SGCPs' kernel hyperparameters between the server and clients, while keeping client-specific parameters local to ensure privacy and personalization. FedPP effectively captures event uncertainty and sparsity, and extensive experiments demonstrate its superior performance in federated settings, particularly with KL divergence and Wasserstein distance-based global aggregation.
Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum likelihood estimation (MLE). Some existing works have proposed score matching estimators for point processes. However, this work demonstrates that the incompleteness of the estimators proposed in those works renders them applicable only to specific problems, and they fail for more general point processes. To address this issue, this work introduces the weighted score matching estimator to point processes. Theoretically, we prove the consistency of our estimator and establish its rate of convergence. Experimental results indicate that our estimator accurately estimates model parameters on synthetic data and yields results consistent with MLE on real data. In contrast, existing score matching estimators fail to perform effectively. Codes are publicly available at \url{https://github.com/KenCao2007/WSM_TPP}.
Temporal point processes (TPPs) are widely used to model the timing and occurrence of events in domains such as social networks, transportation systems, and e-commerce. In this paper, we introduce TPP-LLM, a novel framework that integrates large language models (LLMs) with TPPs to capture both the semantic and temporal aspects of event sequences. Unlike traditional methods that rely on categorical event type representations, TPP-LLM directly utilizes the textual descriptions of event types, enabling the model to capture rich semantic information embedded in the text. While LLMs excel at understanding event semantics, they are less adept at capturing temporal patterns. To address this, TPP-LLM incorporates temporal embeddings and employs parameter-efficient fine-tuning (PEFT) methods to effectively learn temporal dynamics without extensive retraining. This approach improves both predictive accuracy and computational efficiency. Experimental results across diverse real-world datasets demonstrate that TPP-LLM outperforms state-of-the-art baselines in sequence modeling and event prediction, highlighting the benefits of combining LLMs with TPPs.
The standard paradigm of modeling marked point processes is by parameterizing the intensity function using an attention-based (Transformer-style) architecture. Despite the flexibility of these methods, their inference is based on the computationally intensive thinning algorithm. In this work, we propose a framework where the advantages of the attention-based architecture are maintained and the limitation of the thinning algorithm is circumvented. The framework depends on modeling the conditional distribution of inter-event times with a mixture of log-normals satisfying a Markov property and the conditional probability mass function for the marks with a Transformer-based architecture. The proposed method attains state-of-the-art performance in predicting the next event of a sequence given its history. The experiments also reveal the efficacy of the methods that do not rely on the thinning algorithm during inference over the ones they do. Finally, we test our method on the challenging long-horizon prediction task and find that it outperforms a baseline developed specifically for tackling this task; importantly, inference requires just a fraction of time compared to the thinning-based baseline.
Information popularity prediction is important yet challenging in various domains, including viral marketing and news recommendations. The key to accurately predicting information popularity lies in subtly modeling the underlying temporal information diffusion process behind observed events of an information cascade, such as the retweets of a tweet. To this end, most existing methods either adopt recurrent networks to capture the temporal dynamics from the first to the last observed event or develop a statistical model based on self-exciting point processes to make predictions. However, information diffusion is intrinsically a complex continuous-time process with irregularly observed discrete events, which is oversimplified using recurrent networks as they fail to capture the irregular time intervals between events, or using self-exciting point processes as they lack flexibility to capture the complex diffusion process. Against this background, we propose ConCat, modeling the Continuous-time dynamics of Cascades for information popularity prediction. On the one hand, it leverages neural Ordinary Differential Equations (ODEs) to model irregular events of a cascade in continuous time based on the cascade graph and sequential event information. On the other hand, it considers cascade events as neural temporal point processes (TPPs) parameterized by a conditional intensity function which can also benefit the popularity prediction task. We conduct extensive experiments to evaluate ConCat on three real-world datasets. Results show that ConCat achieves superior performance compared to state-of-the-art baselines, yielding a 2.3%-33.2% improvement over the best-performing baselines across the three datasets.
Retrieval-Augmented Generation (RAG) has greatly improved large language models (LLMs) by enabling them to generate accurate, contextually grounded responses through the integration of external information. However, conventional RAG approaches, which prioritize top-ranked documents based solely on query-context relevance, often introduce redundancy and conflicting information. This issue is particularly evident in unsupervised retrieval settings, where there are no mechanisms to effectively mitigate these problems, leading to suboptimal context selection. To address this, we propose Selection using Matrices for Augmented Retrieval (SMART) in question answering tasks, a fully unsupervised and training-free framework designed to optimize context selection in RAG. SMART leverages Determinantal Point Processes (DPPs) to simultaneously model relevance, diversity and conflict, ensuring the selection of potentially high-quality contexts. Experimental results across multiple datasets demonstrate that SMART significantly enhances QA performance and surpasses previous unsupervised context selection methods, showing a promising strategy for RAG.
Quantifying the predictive capacity of a neural system, intended as the capability to store information and actively use it for dynamic system evolution, is a key component of neural information processing. Information storage (IS), the main measure quantifying the active utilization of memory in a dynamic system, is only defined for discrete-time processes. While recent theoretical work laid the foundations for the continuous-time analysis of the predictive capacity stored in a process, methods for the effective computation of the related measures are needed to favor widespread utilization on neural data. This work introduces a method for the model-free estimation of the so-called memory utilization rate (MUR), the continuous-time counterpart of the IS, specifically designed to quantify the predictive capacity stored in neural point processes. The method employs nearest-neighbor entropy estimation applied to the inter-spike intervals measured from point-process realizations to quantify the extent of memory used by a spike train. An empirical procedure based on surrogate data is implemented to compensate the estimation bias and detect statistically significant levels of memory. The method is validated in simulated Poisson processes and in realistic models of coupled cortical dynamics and heartbeat dynamics. It is then applied to real spike trains reflecting central and autonomic nervous system activities: in spontaneously growing cortical neuron cultures, the MUR detected increasing memory utilization across maturation stages, associated to emergent bursting synchronized activity; in the study of the neuro-autonomic modulation of human heartbeats, the MUR reflected the sympathetic activation occurring with postural but not with mental stress. The proposed approach offers a computationally reliable tool to analyze spike train data in computational neuroscience and physiology.
Long-horizon event forecasting is critical across various domains, including retail, finance, healthcare, and social networks. Traditional methods, such as Marked Temporal Point Processes (MTPP), often rely on autoregressive models to predict multiple future events. However, these models frequently suffer from issues like converging to constant or repetitive outputs, which limits their effectiveness and general applicability. To address these challenges, we introduce DeTPP (Detection-based Temporal Point Processes), a novel approach inspired by object detection techniques from computer vision. DeTPP employs a unique matching-based loss function that selectively prioritizes reliably predictable events, improving the accuracy and diversity of predictions during inference. Our method establishes a new state-of-the-art in long-horizon event forecasting, achieving up to a 77% relative improvement over existing MTPP and next-K methods. The proposed hybrid approach enhances the accuracy of next event prediction by up to 2.7% on a large transactional dataset. Notably, DeTPP is also among the fastest methods for inference. The implementation of DeTPP is publicly available on GitHub.
Low Earth orbit (LEO) satellite networks with mega constellations have the potential to provide 5G and beyond services ubiquitously. However, these networks may introduce mutual interference to both satellite and terrestrial networks, particularly when sharing spectrum resources. In this paper, we present a system-level performance analysis to address these interference issues using the tool of stochastic geometry. We model the spatial distributions of satellites, satellite users, terrestrial base stations (BSs), and terrestrial users using independent Poisson point processes on the surfaces of concentric spheres. Under these spatial models, we derive analytical expressions for the ergodic spectral efficiency of uplink (UL) and downlink (DL) satellite networks when they share spectrum with both UL and DL terrestrial networks. These derived ergodic expressions capture comprehensive network parameters, including the densities of satellite and terrestrial networks, the path-loss exponent, and fading. From our analysis, we determine the conditions under which spectrum sharing with UL terrestrial networks is advantageous for both UL and DL satellite networks. Our key finding is that the optimal spectrum sharing configuration among the four possible configurations depends on the density ratio between terrestrial BSs and users, providing a design guideline for spectrum management. Simulation results confirm the accuracy of our derived expressions.
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance point process to the family of homogeneous Poisson point processes, which enables us to generate quickly independent samples of the importance point process. The optimal intensity of the importance point process is found by applying the cross-entropy minimization method. In the proposed scheme, the expected value of the function and the optimal intensity are iteratively estimated in an adaptive manner. We show that the proposed estimator converges to the target value almost surely, and prove the asymptotic normality of it. We explain how to apply the proposed scheme to the estimation of the intensity of a stationary pairwise interaction point process. The performance of the proposed scheme is compared numerically with the Markov chain Monte Carlo simulation and the perfect sampling.
We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a short time interval is negligible, the bursting intensity causes an extreme clustering of events around the singularity. We propose a nonparametric approach to detect such bursts in the intensity. It relies on a heavy traffic condition, which admits inference for point processes over a finite time interval. With Monte Carlo evidence, we show that our testing procedure exhibits size control under the null, whereas it has high rejection rates under the alternative. We implement our approach on high-frequency data for the EUR/USD spot exchange rate, where the test statistic captures abnormal surges in trading activity. We detect a nontrivial amount of intensity bursts in these data and describe their basic properties. Trading activity during an intensity burst is positively related to volatility, illiquidity, and the probability of observing a drift burst. The latter effect is reinforced if the order flow is imbalanced or the price elasticity of the limit order book is large.
Reconfigurable intelligent surfaces (RISs) provide alternative routes for reflected signals to network users, offering numerous applications. This paper explores an innovative approach of strategically deploying RISs along road areas to leverage various propagation and blockage conditions present in cellular networks with roads. To address the local network geometries shown by such networks, we use a stochastic geometry framework, specifically the Cox point processes, to model the locations of RISs and vehicle users. Then, we define the coverage probability as the chance that either a base station or an RIS is in line of sight (LOS) of the typical user and that the LOS signal has a signal-to-noise ratio (SNR) greater than a threshold. We derive the coverage probability as a function of key parameters such as RIS density and path loss exponent. We observe that the network geometry highly affects the coverage and that the proposed RIS deployment effectively leverages the underlying difference of attenuation and blockage, significantly increasing the coverage of vehicle users in the network. With experimental results addressing the impact of key variables to network performance, this work serves as a versatile tool for designing, analyzing, and optimizing RIS-assisted cellular networks with many vehicles.
Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging to seamlessly bridge them with a practicable probabilistic model. In this study, we introduce a new family of distributions, named the discrete kernel point process (DKPP), which includes determinantal point processes and parts of Boltzmann machines. We also develop some computational methods for probabilistic operations and inference with DKPPs, such as calculating marginal and conditional probabilities and learning the parameters. Our numerical experiments demonstrate the controllability of positive and negative dependence and the effectiveness of the computational methods for DKPPs.
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals.