Self-exciting hurdle models for terrorist activity

Porter, Michael D.; White, Gentry

doi:10.1214/11-aoas513

Cited by 88 publications

(78 citation statements)

References 45 publications

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“…The Hawkes self-exciting process [9,10] is a point process model used widely in areas such as neuroscience, seismology, finance, social science, marketing research, and criminology [5,17,3,6,11,7,14,19]. Statistical inference for the classical Hawkes process and its spatial-temporal variant has been studied widely; see e.g.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Estimation for Self-Exciting Point Processes—A Parsimonious Approach

Chen

Hall

2016

Journal of Computational and Graphical Statistics

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There is ample evidence that in applications of self-exciting point-process models, the intensity of background events is often far from constant. If a constant background is imposed, that assumption can reduce significantly the quality of statistical analysis, in problems as diverse as modelling the after-shocks of earthquakes and the study of ultra-high frequency financial data. Parametric models can be used to alleviate this problem, but they run the risk of distorting inference by misspecifying the nature of the background intensity function. On the other hand, a purely nonparametric approach to analysis leads to problems of identifiability; when a nonparametric approach is taken, not every aspect of the model can be identified from data recorded along a single observed sample path. In this paper we suggest overcoming this difficulty by using an approach based on the principle of parsimony, or Occam's Razor. In particular, we suggest taking the pointprocess intensity to be either a constant, or to have maximum differential entropy, in cases where there is not sufficient empirical evidence to suggest that the background intensity function is more complex than those models. This approach is seldom, if ever, used for nonparametric function estimation in other settings, not least because in those cases more data are typically available. However, our "ontological parsimony" argument is appropriate in the context of self-exciting pointprocess models. Supplementary materials are available online.

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Section: Introductionmentioning

confidence: 99%

Nonparametric Estimation for Self-Exciting Point Processes—A Parsimonious Approach

Chen

Hall

2016

Journal of Computational and Graphical Statistics

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“…People find self-exciting point processes naturally suitable to model continuous-time events where the occurrence of one event can affect the likelihood of subsequent events in the future. One important self-exciting process is Hawkes process, which is first used to analyze earthquakes [25,37], and then widely applied to many different areas, such as market modeling [13,3], crime modeling [29], terrorist [26], conflict [35,21], and viral videos on the Web [10]. A novel Hawkes model was also proposed to model both temporal and textual information in viral [34].…”

Section: Related Workmentioning

confidence: 99%

Identifying and labeling search tasks via query-based hawkes processes

Deng

Dong

et al. 2014

Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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We consider a search task as a set of queries that serve the same user information need. Analyzing search tasks from user query streams plays an important role in building a set of modern tools to improve search engine performance. In this paper, we propose a probabilistic method for identifying and labeling search tasks based on the following intuitive observations: queries that are issued temporally close by users in many sequences of queries are likely to belong to the same search task, meanwhile, different users having the same information needs tend to submit topically coherent search queries. To capture the above intuitions, we directly model query temporal patterns using a special class of point processes called Hawkes processes, and combine topic models with Hawkes processes for simultaneously identifying and labeling search tasks. Essentially, Hawkes processes utilize their self-exciting properties to identify search tasks if influence exists among a sequence of queries for individual users, while the topic model exploits query co-occurrence across different users to discover the latent information needed for labeling search tasks. More importantly, there is mutual reinforcement between Hawkes processes and the topic model in the unified model that enhances the performance of both. We evaluate our method based on both synthetic data and real-world query log data. In addition, we also apply our model to query clustering and search task identification. By comparing with state-of-the-art methods, the results demonstrate that the improvement in our proposed approach is consistent and promising.

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“…One important self-exciting process is the Hawkes process, which was first used to analyze earthquakes [13], and later applied to a wide range of tasks such as market modeling [5, 2], crime modeling [16], terrorist [14], conflict [18], and viral videos on the Web [4]. An EM framework was proposed to estimate the maximum likelihood of Hawkes processes [11].…”

Section: Related Workmentioning

confidence: 99%

Dyadic event attribution in social networks with mixtures of hawkes processes

Zha

2013

Proceedings of the 22nd ACM International Conference on Information &Amp; Knowledge Management

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In many applications in social network analysis, it is important to model the interactions and infer the influence between pairs of actors, leading to the problem of dyadic event modeling which has attracted increasing interests recently. In this paper we focus on the problem of dyadic event attribution, an important missing data problem in dyadic event modeling where one needs to infer the missing actor-pairs of a subset of dyadic events based on their observed timestamps. Existing works either use fixed model parameters and heuristic rules for event attribution, or assume the dyadic events across actor-pairs are independent. To address those shortcomings we propose a probabilistic model based on mixtures of Hawkes processes that simultaneously tackles event attribution and network parameter inference, taking into consideration the dependency among dyadic events that share at least one actor. We also investigate using additive models to incorporate regularization to avoid overfitting. Our experiments on both synthetic and real-world data sets on international armed conflicts suggest that the proposed new method is capable of significantly improve accuracy when compared with the state-of-the-art for dyadic event attribution.

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Self-exciting hurdle models for terrorist activity

Cited by 88 publications

References 45 publications

Nonparametric Estimation for Self-Exciting Point Processes—A Parsimonious Approach

Nonparametric Estimation for Self-Exciting Point Processes—A Parsimonious Approach

Identifying and labeling search tasks via query-based hawkes processes

Dyadic event attribution in social networks with mixtures of hawkes processes

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