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1. Interpretable Hawkes Process Spatial Crime Forecasting with TV-Regularization

   Sha, H.; Hasan, M.; Carter, J.G.; Mohler, G. (January 2020, IEEE International Conference on Big Data)

   null (Ed.)

   Interpretable models for criminal justice forecasting are desirable due to the high-stakes nature of the application. While interpretable models have been developed for individual level forecasts of recidivism, interpretable models are lacking for the application of space-time crime hotspot forecasting. Here we introduce an interpretable Hawkes process model of crime that allows forecasts to capture near-repeat effects and spatial heterogeneity while being consumable in the form of easy-to-read score cards. For this purpose we employ penalized likelihood estimation of the point process with a total-variation regularization that enforces the triggering kernel to be piece-wise constant. We derive an efficient expectation-maximization algorithm coupled with forward backward splitting for the TV constraint to estimate the model. We apply our methodology to synthetic data and space-time crime data from Indianapolis. The TV-Hawkes process achieves similar accuracy to standard Hawkes process models of crime while increasing interpretability and transparency. 

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2. The Multivariate Community Hawkes model for dependent relational events in continuous-time networks

   Soliman, Hadeel; Zhao, Lingfei; Huang, Zhipeng; Paul, Subhadeep; Xu, Kevin S. (January 2022, Proceedings of Machine Learning Research)

   The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks. 

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3. A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering

   Xu, Hongteng; Zha, Hongyuan (January 2017, Advances in neural information processing systems)

   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 distribution 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. 

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4. A mutually exciting latent space Hawkes process model for continuous-time networks

   Huang, Zhipeng; Soliman, Hadeel; Paul, Subhadeep; Xu, Kevin S. (January 2022, Proceedings of Machine Learning Research)

   Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models. 

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5. Modeling Sequential Online Interactive Behaviors with Temporal Point Process

   https://doi.org/10.1145/3269206.3271782  

   Cai, Renqin; Bai, Xueying; Wang, Zhenrui; Shi, Yuling; Sondhi, Parikshit; Wang, Hongning (October 2018, Proceedings of the 27th ACM International Conference on Information and Knowledge Management)

   The massively available data about user engagement with online information service systems provides a gold mine about users' latent intents. It calls for quantitative user behavior modeling. In this paper, we study the problem by looking into users' sequential interactive behaviors. Inspired by the concepts of episodic memory and semantic memory in cognitive psychology, which describe how users' behaviors are differently influenced by past experience, we propose a Long- and Short-term Hawkes Process model. It models the short-term dependency between users' actions within a period of time via a multi-dimensional Hawkes process and the long-term dependency between actions across different periods of time via a one dimensional Hawkes process. Experiments on two real-world user activity log datasets (one from an e-commerce website and one from a MOOC website) demonstrate the effectiveness of our model in capturing the temporal dependency between actions in a sequence of user behaviors. It directly leads to improved accuracy in predicting the type and the time of the next action. Interestingly, the inferred dependency between actions in a sequence sheds light on the underlying user intent behind direct observations and provides insights for downstream applications. 

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