A Higher-Order Singular Value Decomposition Tensor Emulator for Spatiotemporal Simulators

Gopalan, Giri; Wikle, Christopher K.

doi:10.1007/s13253-021-00459-x

Cited by 5 publications

(5 citation statements)

References 30 publications

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“…We provide a brief overview of the necessary background in Web Appendix C . We first describe our methodology in Sections 3.1 and 3.2 in terms of the higher-order singular value decompositions (HOSVD) of tensors, as in Gopalan and Wikle ( 2022 ). In Section 3.3 , we discuss our imputation methodology for arbitrary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $ {\boldsymbol \theta }^{*} \notin \lbrace {\boldsymbol \theta }_1,..., {\boldsymbol \theta }_K\rbrace$\end{document} .…”

Section: Emulator For the Mean And Covariance Functionsmentioning

confidence: 99%

“…( 2014 ). Recently Pratola and Chkrebtii ( 2018 ) and Gopalan and Wikle ( 2022 ) extended SVD-based approaches to computational output stored in tensors, an approach we adapt in this paper. Many other approaches to constructing emulators are possible, however (eg, Reich et al., 2012 ; Massoud, 2019 ; Thakur and Chakraborty, 2022 ).…”

Section: Introductionmentioning

confidence: 99%

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A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

Trostle,

Guinness,

Reich

2024

Biometrics

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The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the well-known SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.

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Section: Emulator For the Mean And Covariance Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

Trostle,

Guinness,

Reich

2024

Biometrics

View full text Add to dashboard Cite

show abstract

“…The authors show that the CVAE can be used to effectively predict the output of the LPDM over a wide spatial domain given only a few simulations, and that the CVAE considerably outperforms the conventional emulator based on singular vectors (e.g., Hooten et al, 2011). Recently, Gopalan & Wikle (2022) extended the singular vector approach to higher-order tensor decompositions to emulate complex multi-dimensional spatio-temporal data, including the movement trajectories of agents in an agent-based model. Their approach is flexible in that different machine learning methods (e.g., random forests and neural networks) or GP regression models can be used in the various tensor dimensions.…”

Section: Deep Emulationmentioning

confidence: 99%

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Wikle¹,

Zammit‐Mangion²

2022

Preprint

Self Cite

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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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“…Much of the discussion in this section will use tensor terminology and notation. We provide a brief overview of the necessary background in Appendix C. We first describe our methodology in Sections 3.1 and 3.2 in terms of the higher-order singular value decompositions (HOSVD) of tensors, as in Gopalan and Wikle (2022). In Section 3.3 we discuss our imputation methodology for arbitrary θ * / ∈ {θ 1 , ..., θ K }.…”

Section: Emulator For the Mean And Covariance Functionsmentioning

confidence: 99%

“…This approach was extended in Hooten et al (2011) and Leeds et al (2014). Recently Pratola and Chkrebtii (2018) and Gopalan and Wikle (2022) extended these SVD-based approaches to computational output stored in tensors, an approach we adapt in this paper. Many other approaches to constructing emulators are possible, however (e.g., Gu et al, 2018;Massoud, 2019;Thakur and Chakraborty, 2022;Reich et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

Trostle¹,

Guinness²,

Reich³

2022

Preprint

View full text Add to dashboard Cite

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the wellknown SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.

show abstract

A Higher-Order Singular Value Decomposition Tensor Emulator for Spatiotemporal Simulators

Cited by 5 publications

References 30 publications

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

Statistical Deep Learning for Spatial and Spatio-Temporal Data

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators

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