Gaussian Processes in Practice, PMLR 1:73-89, 2007.
Abstract
Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.
@InProceedings{pmlr-v1-vanhatalo07a,
title = {Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology},
author = {Jarno Vanhatalo and Aki Vehtari},
booktitle = {Gaussian Processes in Practice},
pages = {73--89},
year = {2007},
editor = {Neil D. Lawrence and Anton Schwaighofer and Joaquin Quiñonero Candela},
volume = {1},
series = {Proceedings of Machine Learning Research},
address = {Bletchley Park, UK},
month = {12--13 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v1/vanhatalo07a/vanhatalo07a.pdf},
url = {http://proceedings.mlr.press/v1/vanhatalo07a.html},
abstract = {Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.}
}
%0 Conference Paper
%T Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology
%A Jarno Vanhatalo
%A Aki Vehtari
%B Gaussian Processes in Practice
%C Proceedings of Machine Learning Research
%D 2007
%E Neil D. Lawrence
%E Anton Schwaighofer
%E Joaquin Quiñonero Candela
%F pmlr-v1-vanhatalo07a
%I PMLR
%J Proceedings of Machine Learning Research
%P 73--89
%U http://proceedings.mlr.press
%V 1
%W PMLR
%X Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.
TY - CPAPER
TI - Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology
AU - Jarno Vanhatalo
AU - Aki Vehtari
BT - Gaussian Processes in Practice
PY - 2007/03/11
DA - 2007/03/11
ED - Neil D. Lawrence
ED - Anton Schwaighofer
ED - Joaquin Quiñonero Candela
ID - pmlr-v1-vanhatalo07a
PB - PMLR
SP - 73
DP - PMLR
EP - 89
L1 - http://proceedings.mlr.press/v1/vanhatalo07a/vanhatalo07a.pdf
UR - http://proceedings.mlr.press/v1/vanhatalo07a.html
AB - Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.
ER -
Vanhatalo, J. & Vehtari, A.. (2007). Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology. Gaussian Processes in Practice, in PMLR 1:73-89
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