Home > Research > Publications & Outputs > Spatial Analysis Made Easy with Linear Regressi...

Electronic data

  • 1902.08679

    Accepted author manuscript, 1.58 MB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Links

Text available via DOI:

View graph of relations

Spatial Analysis Made Easy with Linear Regression and Kernels

Research output: Contribution to journalJournal article

Published

Standard

Spatial Analysis Made Easy with Linear Regression and Kernels. / Milton, Philip; Coupland, Helen; Giorgi, Emanuele; Bhatt, Samir.

In: Epidemics, Vol. 29, 100362, 31.12.2019.

Research output: Contribution to journalJournal article

Harvard

APA

Vancouver

Author

Milton, Philip ; Coupland, Helen ; Giorgi, Emanuele ; Bhatt, Samir. / Spatial Analysis Made Easy with Linear Regression and Kernels. In: Epidemics. 2019 ; Vol. 29.

Bibtex

@article{2a06eaae5f324cd38a7a507bca388a86,
title = "Spatial Analysis Made Easy with Linear Regression and Kernels",
abstract = "Kernel methods are a popular technique for extending linear models to handle non-linear spatial problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature mapping, they are still subject to cubic cost on the number of points. Given only a few thousand locations, this computational cost rapidly outstrips the currently available computational power. This paper aims to provide an overview of kernel methods from first-principals (with a focus on ridge regression) and progress to a review of random Fourier features (RFF), a method that enables the scaling of kernel methods to big datasets. We show how the RFF method is capable of approximating the full kernel matrix, providing a significant computational speed-up for a negligible cost to accuracy and can be incorporated into many existing spatial methods using only a few lines of code. We give an example of the implementation of RFFs on a simulated spatial data set to illustrate these properties. Lastly, we summarise the main issues with RFFs and highlight some of the advanced techniques aimed at alleviating them. At each stage, the associated R code is provided.",
keywords = "Regression, Random Fourier features, Kernel methods, Kernel approximation",
author = "Philip Milton and Helen Coupland and Emanuele Giorgi and Samir Bhatt",
year = "2019",
month = dec
day = "31",
doi = "10.1016/j.epidem.2019.100362",
language = "English",
volume = "29",
journal = "Epidemics",
issn = "1755-4365",
publisher = "ELSEVIER SCIENCE BV",

}

RIS

TY - JOUR

T1 - Spatial Analysis Made Easy with Linear Regression and Kernels

AU - Milton, Philip

AU - Coupland, Helen

AU - Giorgi, Emanuele

AU - Bhatt, Samir

PY - 2019/12/31

Y1 - 2019/12/31

N2 - Kernel methods are a popular technique for extending linear models to handle non-linear spatial problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature mapping, they are still subject to cubic cost on the number of points. Given only a few thousand locations, this computational cost rapidly outstrips the currently available computational power. This paper aims to provide an overview of kernel methods from first-principals (with a focus on ridge regression) and progress to a review of random Fourier features (RFF), a method that enables the scaling of kernel methods to big datasets. We show how the RFF method is capable of approximating the full kernel matrix, providing a significant computational speed-up for a negligible cost to accuracy and can be incorporated into many existing spatial methods using only a few lines of code. We give an example of the implementation of RFFs on a simulated spatial data set to illustrate these properties. Lastly, we summarise the main issues with RFFs and highlight some of the advanced techniques aimed at alleviating them. At each stage, the associated R code is provided.

AB - Kernel methods are a popular technique for extending linear models to handle non-linear spatial problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature mapping, they are still subject to cubic cost on the number of points. Given only a few thousand locations, this computational cost rapidly outstrips the currently available computational power. This paper aims to provide an overview of kernel methods from first-principals (with a focus on ridge regression) and progress to a review of random Fourier features (RFF), a method that enables the scaling of kernel methods to big datasets. We show how the RFF method is capable of approximating the full kernel matrix, providing a significant computational speed-up for a negligible cost to accuracy and can be incorporated into many existing spatial methods using only a few lines of code. We give an example of the implementation of RFFs on a simulated spatial data set to illustrate these properties. Lastly, we summarise the main issues with RFFs and highlight some of the advanced techniques aimed at alleviating them. At each stage, the associated R code is provided.

KW - Regression

KW - Random Fourier features

KW - Kernel methods

KW - Kernel approximation

U2 - 10.1016/j.epidem.2019.100362

DO - 10.1016/j.epidem.2019.100362

M3 - Journal article

VL - 29

JO - Epidemics

JF - Epidemics

SN - 1755-4365

M1 - 100362

ER -