Neural Spatio-Temporal Point Processes

Chen, Ricky T. Q.; Amos, Brandon; Nickel, Maximilian

doi:10.48550/arxiv.2011.04583

Cited by 5 publications

(6 citation statements)

References 36 publications

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“…It is natural to expect that including spatial covariates would improve forecasting performance (Utsu, 1955;Ogata, 1998), however, it is not clear that considering them as an additional dimension to the input of an RNN would learn any spatial structure from the data. Neural point processes for spatio-temporal data do not utilise RNNs which are primarily sequence encoders and instead consider models based on Ordinary Differential Equations (ODEs) (Chen et al, 2020;Biloš et al, 2021). We believe such models should outperform RNN-based models on spatio-temporal data.…”

Section: Limitationsmentioning

confidence: 99%

Forecasting the 2016-2017 Central Apennines Earthquake Sequence with a Neural Point Process

Stockman¹,

Lawson²,

Werner³

2023

Preprint

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Section: Limitationsmentioning

confidence: 99%

Forecasting the 2016-2017 Central Apennines Earthquake Sequence with a Neural Point Process

Stockman¹,

Lawson²,

Werner³

2023

Preprint

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“…These intensity functions, which are conditional on the event history, are often more applicable to real world processes, such as financial or crime data. Jia & Benson (2019) apply the neural ordinary differential equations of Chen et al (2018) to model conditional intensity functions, while Chen et al (2020) extend the concept to the spatio-temporal case. Zhu et al (2020) take a different approach and directly model the influence of a past point on the intensity function using a Gaussian mixture, where the parameters in each mixture component are the outputs of a simple, one-layer, neural net that take the spatial coordinates as input.…”

Section: Conditional Intensity Function Modelingmentioning

confidence: 99%

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Wikle¹,

Zammit‐Mangion²

2022

Preprint

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Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.

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“…A large body of literature on meta-models (or surrogate models, or emulators) in various disciplines focuses on Gaussian processes or machine-learning techniques (Forrester et al 2008, Kleijnen 2015. Discrete events data localized in continuous time and space are also assessed through machine learning (Reinhart 2018, Chen et al 2020, Zhu et al 2020, Dong et al 2021. For example, Du et al (2016) and Zhang et al (2020) model discrete events using neural-network-based point process models with the aim of presenting highly performing approaches for reproducing and predicting spatio-temporal patterns observed in the data.…”

Section: Predictive Performancementioning

confidence: 99%

Understanding complex spatial dynamics from mechanistic models through spatio‐temporal point processes

et al. 2022

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Landscape heterogeneity affects population dynamics, which determine species persistence, diversity and interactions. These relationships can be accurately represented by advanced spatially-explicit models (SEMs) allowing for high levels of detail and precision. However, such approaches are characterised by high computational complexity, high amount of data and memory requirements and spatio-temporal outputs may be difficult to analyse. A possibility to deal with this complexity is to aggregate outputs over time or space, but then interesting information may be masked and lost, such as local spatio-temporal relationships or patterns. An alternative solution is given by meta-models and meta-analysis, where simplified mathematical relationships are used to structure and summarise the complex transformations from inputs to outputs. Here, we propose an original approach to analyse SEM outputs. By developing a metamodelling approach based on spatio-temporal point processes (STPPs), we characterise spatio-temporal population dynamics and landscape heterogeneity relationships in agricultural contexts. A landscape generator and a spatially-explicit population model simulate hierarchically the pest-predator dynamics of codling moth and ground beetles in apple orchards over heterogeneous agricultural landscapes. Spatio-temporally explicit outputs are simplified to marked point patterns of key events, such as local proliferation or introduction events. Then, we construct and estimate regression equations for multi-type STPPs composed of event occurrence intensity and magnitudes. Results provide local insights into spatio-temporal dynamics of pest-predator systems. We are able to differentiate the contributions of different driver categories (i.e. spatiotemporal, spatial, population dynamics). We highlight changes in the effects on occurrence intensity and magnitude when considering drivers at global or local scale. This approach leads to novel findings in agroecology where, for example, we show that the organisation of cultivated patches and semi-natural elements play different roles for pest regulation depending on the scale considered. It aids to formulate guidelines for biological control strategies at global and local scale.

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Neural Spatio-Temporal Point Processes

Cited by 5 publications

References 36 publications

Forecasting the 2016-2017 Central Apennines Earthquake Sequence with a Neural Point Process

Forecasting the 2016-2017 Central Apennines Earthquake Sequence with a Neural Point Process

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Understanding complex spatial dynamics from mechanistic models through spatio‐temporal point processes

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