Learning Multivariate Hawkes Processes at Scale

Nickel, Maximilian; Le, Matthew

doi:10.48550/arxiv.2002.12501

Cited by 9 publications

(16 citation statements)

References 19 publications

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“…Unfortunately, the current model will fail when applied to the analysis of a global pandemic due to the dominant role of non-local, large scale transportation networks in propagating viral spread (Holbrook et al, 2020). We are particularly interested in developing extensions to the phylogenetic Hawkes process that leverage recent advances in scaling highdimensional multivariate Hawkes processes (Nickel and Le, 2020) and applying the resulting multivariate phylogenetic Hawkes process to the analysis of global pandemics. In this context, each additional dimension will represent an additional country or province.…”

Section: Discussionmentioning

confidence: 99%

From viral evolution to spatial contagion: a biologically modulated Hawkes model

Holbrook¹,

Xiang²,

Suchard³

2021

Preprint

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Mutations sometimes increase contagiousness for evolving pathogens. During an epidemic, epidemiologists use viral genetics to infer a shared evolutionary history and connect this history to geographic spread. We propose a model that directly relates a pathogen's evolution to its spatial contagion dynamics-effectively combining the two epidemiological paradigms of phylogenetic inference and self-exciting process modeling-and apply this phylogenetic Hawkes process to a Bayesian analysis of 23,422 viral cases from the 2014-2016 Ebola outbreak in West Africa. With a mere 1,610 samples providing RNA data, our model is able to detect subsets of the Ebola virus with significantly elevated rates of spatiotemporal propagation.

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Section: Discussionmentioning

confidence: 99%

From viral evolution to spatial contagion: a biologically modulated Hawkes model

Holbrook¹,

Xiang²,

Suchard³

2021

Preprint

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“…• Reddit: We crawled the official Reddit API 1 to gather timestamped hyperlinks between Reddit communities (i.e., subreddits) over 6 months from March 1 to August 31, 2020. Following the work of [24], we use a list of hyperlinks to each target subreddit as a separate sequence and consider target subreddits as communities (i.e., dimensions). All the datasets are publicly available.…”

Section: Datasetsmentioning

confidence: 99%

Dynamic Hawkes Processes for Discovering Time-evolving Communities' States behind Diffusion Processes

Okawa,

Iwata,

Tanaka

et al. 2021

Preprint

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Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g., regions, online user groups). Modeling diffusion processes and predicting future events are crucial in many applications including epidemic control, viral marketing, and predictive policing. Hawkes processes offer a central tool for modeling the diffusion processes, in which the influence from the past events is described by the triggering kernel. However, the triggering kernel parameters, which govern how each community is influenced by the past events, are assumed to be static over time. In the real world, the diffusion processes depend not only on the influences from the past, but also the current (time-evolving) states of the communities, e.g., people's awareness of the disease and people's current interests. In this paper, we propose a novel Hawkes process model that is able to capture the underlying dynamics of community states behind the diffusion processes and predict the occurrences of events based on the dynamics. Specifically, we model the latent dynamic function that encodes these hidden dynamics by a mixture of neural networks. Then we design the triggering kernel using the latent dynamic function and its integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a flexible way to learn complex representations of the time-evolving communities' states, while at the same time it allows to computing the exact likelihood, which makes parameter learning tractable. Extensive experiments on four real-world event datasets show that DHP outperforms five widely adopted methods for event prediction.

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“…Recent progress has been made in factorizing interactions with a direct focus on scalability [19], improving on prior work in low-rank processes [20]. Block models on observed interaction pairs also exist [21].…”

Section: Related Workmentioning

confidence: 99%

“…One active line of work, paralleling ours, embeds each event based on some conceived heuristic like temporal proximity [16,17,18]; another direction of inquiry entails the estimation of low-rank multivariate Hawkes processes [19,20,21]. We differ from both in learning an actual metric-space representation vis-à-vis the real Hawkes likelihood.…”

Section: Introductionmentioning

confidence: 99%

A Metric Space for Point Process Excitations

Marmarelis,

Steeg,

Galstyan

2020

Preprint

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When specific events seem to spur others in their wake, marked Hawkes processes enable us to reckon with their statistics. The underdetermined empirical nature of these event-triggering mechanisms hinders estimation in the multivariate setting. Spatiotemporal applications alleviate this obstacle by allowing relationships to depend only on relative distances in real Euclidean space; we employ the framework as a vessel for embedding arbitrary event types in a new latent space. By performing synthetic experiments on short records as well as an investigation into options markets and pathogens, we demonstrate that learning the embedding alongside a point process model uncovers the coherent, rather than spurious, interactions.Preprint. Under review.

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Learning Multivariate Hawkes Processes at Scale

Cited by 9 publications

References 19 publications

From viral evolution to spatial contagion: a biologically modulated Hawkes model

From viral evolution to spatial contagion: a biologically modulated Hawkes model

Dynamic Hawkes Processes for Discovering Time-evolving Communities' States behind Diffusion Processes

A Metric Space for Point Process Excitations

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