The generative mechanisms behind real-world event sequences are often heterogeneous, leading to data that possesses inherent clustering structures. However, most existing temporal point processes (TPPs) treat different event sequences independently, without leveraging the clustering structures when predicting events. In this study, we design and learn a novel semi-transductive temporal point process (ST-TPP), which explicitly improves prediction performance by co-training sequence clusters. In particular, given a set of event sequences, our method learns a neural TPP together with cluster centers of the sequences. Besides maximizing the likelihood of the event sequences, we leverage a data-based kernel matrix and prior knowledge to regularize the sequence embeddings, leading to a Gromov-Wasserstein barycentric (GWB) regularizer. Based on the optimal transport plans associated with the GWB regularizer, we derive the cluster centers by the push-forward of the sequence embeddings. When a new sequence comes, the learned model first assigns a cluster center to the sequence and then jointly encodes the sequence and the cluster center to predict future events, leading to a semi-transductive prediction scheme. Experiments demonstrate that ST-TPP achieves competitive sequence clustering results and strong prediction performance.

An event sequence generated by a temporal point process is often associated with a hidden and structured event branching process that captures the triggering relations between its historical and current events. In this study, we design a new plug-and-play module based on the Bregman ADMM (BADMM) algorithm, which infers event branches associated with event sequences in the maximum likelihood estimation framework of temporal point processes (TPPs). Specifically, we formulate the inference of event branches as an optimization problem of event transition matrix under sparse and low-rank constraints, which is embedded in existing TPP models or their learning paradigms. We can implement this optimization problem based on subspace clustering and sparse group-lasso, respectively, and solve it using the Bregman ADMM algorithm, whose unrolling leads to the proposed BADMM module. When learning a classic TPP (e.g., Hawkes process) by the expectation-maximization algorithm, the BADMM module helps derive structured responsibility matrices in the E-step. Similarly, the BADMM module helps derive low-rank and sparse attention maps for the neural TPPs with self-attention layers. The structured responsibility matrices and attention maps, which work as learned event transition matrices, indicate event branches, e.g., inferring isolated events and those key events triggering many subsequent events. Experiments on both synthetic and real-world data show that plugging our BADMM module into existing TPP models and learning paradigms can improve model performance and provide us with interpretable structured event branches.

Latency, as a critical attribute influencing scalability and consistency in blockchain systems, has attracted significant research attention. This paper addresses the issue of latency evaluation by presenting a novel framework. We thoroughly analyze the factors affecting latency in blockchain system, including concurrency, consistency, and contention. To accurately model the correlation between latency and the quantity of nodes in permissioned blockchain setup, we introduce the Latency Regression Loss (LRL) function. By utilizing Newton’s interpolation and least squares methods, we determine the hyperparameters. Subsequently, we devise the framework for the Quantitative Dynamic Latency (QDL) evaluation model, which accounts for both the growth rate and magnitude of latency. Utilizing the parameters derived from the LRL function facilitated the calculation of latency growth rate, allowing for a comprehensive evaluation of latency. Finally, we validated the accuracy of the LRL function through extensive experiments and simulated the adaptability of the QDL model in latency assessment.

As an important sequential model, the temporal point process (TPP) plays a central role in real-world sequence modeling 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 at the sequence-level 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.

In recent decades, commodities have attracted the attention of a large number of investors and financial professionals, and their prices have become very important for investors and policy makers. Although natural gas is widely used as a clean energy, there is less literature on price research and most of them use historical prices and fundamental factors to analyze natural gas price. Based on historical prices, this paper analyzes whether internet search data and news sentiment can improve forecasting ability, and compare which can achieve better prediction results. The experimental results show that both internet search and news sentiment contain additional information to improve the prediction effect, and internet search data can achieve better prediction results.

Distributed multimedia applications such as video on demand (VoD), require dynamic quality of service (QoS) guarantee from service servers for their continuous multimedia streams. In this paper, we build the service availability Markovian model for unified failure-recovery mechanism under variant load scenarios, by calculating local and global kernels of the Markovain model, we get the steady-state availability and unavailability probabilities. Numerical results show that there exist differences between the system availability and the request perceived availability under variant load state (the nature of this kind of system's scenario). This provides strategies for improving VoD system's availability