How to cluster event sequences generated via different point processes is an interesting and important problem in statistical machine learning. To solve this problem, we propose and discuss an effective model-based clustering method based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. The proposed model generates the event sequences with different clusters from the Hawkes processes with different parameters, and uses a Dirichlet process as the prior distribution of the clusters. We prove the identifiability of our mixture model and propose an effective variational Bayesian inference algorithm to learn our model. An adaptive inner iteration allocation strategy is designed to accelerate the convergence of our algorithm. Moreover, we investigate the sample complexity and the computational complexity of our learning algorithm in depth. Experiments on both synthetic and real-world data show that the clustering method based on our model can learn structural triggering patterns hidden in asynchronous event sequences robustly and achieve superior performance on clustering purity and consistency compared to existing methods.

Such causal graphs delineate the relations among alarms and can significantly aid engineers in identifying and rectifying faults. However, existing methods either ignore the topological relationships among devices or suffer from relatively low scalability and efficiency, failing to deliver high-quality responses in a timely manner.

Despite the flexibility of these methods, their inference is based on the computationally intensive thinning algorithm.

TPP models in density estimation and strongly outperforms them in forecasting.

This dataset covers various topics and is suitable for instruction-tuning general-purpose LLMs for diverse clinical use cases.