Imperial College London
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DrSethFlaxman

Faculty of Natural Sciences, Department of Mathematics

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522Huxley BuildingSouth Kensington Campus

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Publications

Citation

BibTex format

@article{Ton:2018:10.1016/j.spasta.2018.02.002,
author = {Ton, J-F and Flaxman, S and Sejdinovic, D and Bhatt, S},
doi = {10.1016/j.spasta.2018.02.002},
journal = {Spatial Statistics},
pages = {59--78},
title = {Spatial mapping with Gaussian processes and nonstationary Fourier features},
url = {http://dx.doi.org/10.1016/j.spasta.2018.02.002},
volume = {28},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limited class of stationary kernels such as the Matérn or squared exponential, limiting the expressiveness of these modelling approaches. Recent machine learning research has focused on spectral representations to model arbitrary stationary kernels and introduced more general representations that include classes of nonstationary kernels. In this paper, we exploit the connections between Fourier feature representations, Gaussian processes and neural networks to generalise previous approaches and develop a simple and efficient framework to learn arbitrarily complex nonstationary kernel functions directly from the data, while taking care to avoid overfitting using state-of-the-art methods from deep learning. We highlight the very broad array of kernel classes that could be created within this framework. We apply this to a time series dataset and a remote sensing problem involving land surface temperature in Eastern Africa. We show that without increasing the computational or storage complexity, nonstationary kernels can be used to improve generalisation performance and provide more interpretable results.
AU  - Ton,J-F
AU  - Flaxman,S
AU  - Sejdinovic,D
AU  - Bhatt,S
DO  - 10.1016/j.spasta.2018.02.002
EP  - 78
PY  - 2018///
SN  - 2211-6753
SP  - 59
TI  - Spatial mapping with Gaussian processes and nonstationary Fourier features
T2  - Spatial Statistics
UR  - http://dx.doi.org/10.1016/j.spasta.2018.02.002
UR  - https://www.sciencedirect.com/science/article/pii/S2211675317302890?via%3Dihub
UR  - http://hdl.handle.net/10044/1/61634
VL  - 28
ER  -
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