| Version: | 0.3-25 |
| Date: | 2025-09-26 |
| Title: | Projected Spatial Gaussian Process Methods |
| Depends: | R (≥ 3.5.0), intamap |
| Imports: | gstat, automap, sp, doParallel, foreach, parallel, Rcpp |
| Suggests: | sf |
| LinkingTo: | Rcpp, RcppArmadillo (≥ 0.2.0) |
| Description: | Implements projected sparse Gaussian process Kriging ('Ingram et. al.', 2008, <doi:10.1007/s00477-007-0163-9>) as an additional method for the 'intamap' package. More details on implementation ('Barillec et. al.', 2010, <doi:10.1016/j.cageo.2010.05.008>). |
| License: | GPL-2 |GPL-3 [expanded from: GPL (≥ 2)] |
| Repository: | CRAN |
| NeedsCompilation: | yes |
| Packaged: | 2025-09-29 20:28:43 UTC; bri |
| Date/Publication: | 2025-09-29 21:40:02 UTC |
| Maintainer: | Ben Ingram <ingrambr.work@gmail.com> |
| RoxygenNote: | 7.3.2 |
| Author: | Ben Ingram [aut, cre], Remi Barillec [aut], Jon Olav Skoien [aut] |
Projected Sequential Gaussian Processes for spatial interpolation
Description
Thepsgp package provides a spatial interpolation method based on Projected Sequential Gaussian Processes (PSGP) for theintamap package. The PSGP (Csato, 2002) is an approximation to the standard Gaussian process (Rasmussen and Williams, 1996) whereby the observations are projected onto a subset of optimal "active" observations, thus reducing possible redundancy in the data and allowing for faster, memory efficient, interpolation. The projection is done in a sequential manner, that is one observation is projected onto the active subset at a time. This allows for larger datasets to be processed, and overcomes the limitations of standard Gaussian processes related to storing the full covariance matrix (which can be unfeasible for really large datasets).
This implementation of PSGP for spatial interpolation uses a mixture of covariance kernels, namely an Exponential kernel and a Matern kernel with roughness parameter 5/2. The covariance function also includes a nugget term (white noise) and bias term.
Parameter estimation
The methodestimateParameters looks for a set of covariance function parameters (kernels, white noise and bias) which maximisethe likelihood of the observation.
Prediction/Interpolation
The methodspatialPredict computes predictions (including variance) at a set of unobserved locations.
Measurement errors
It is possible to include measurement errors if these are available. These will be taken into account when estimating parameters and making predictions. SeelearnParameters for more information.
System requirements
the PSGP package is written in C++ and uses the Armadillo library for all linear algebra routines.
Author(s)
Ben Ingram, Remi Barillec
References
Csato, L., Gaussian Processes - Iterative Sparse Approximations, Ph.D Thesis, NCRG, Aston University, UK, 2002.
Rasmussen, C. E. and Williams, C. K., Gaussian Processes for Machine Learning, The MIT Press, Cambridge, Massachusetts, 1996.
Build Metadata Table
Description
buildMetadata builds a metadata table of likelihood model descriptors in the PSGP framework. This is an internal function and it should not be used directly.
Usage
buildMetadata(observations)Arguments
observations | an observations data frame containing a vector of observation variances ( |
Details
buildMetadata builds a metadata table of likelihood model descriptors in the PSGP framework. The likelihood models are assumed Gaussian with variances specified in the vectorobservations$oevar (the bias is assumed to be zero). Optionally, biases can be specified in theobservations$oebias vector. However, biases are not taken into account in the current version of the PSGP package (they will be in a future release).
Author(s)
Remi Barillec
See Also
learnParameters,makePrediction,estimateParameters,spatialPredict,
Examples
## Load our favourite dataset data(meuse) obs <- meuse ## Number of observations nobs <- length(obs$y) ## Indicate which likelihood model should be used for each observation obs$oeid <- seq(1:nobs) ## Use random variances for the sake of the example obs$oevar <- rnorm( max(obs$oeid) ) ## Generate metadata table and print it out metadata <- buildMetadata(obs) print(metadata)Parameter estimation using a Projected Sequential Gaussian Process (PSGP)
Description
This overloads theestimateParameters routine from the intamap package for interpolation using the PSGP method.
Usage
estimateParameters(object, ...)Arguments
object | a list object of Intamap type. Most arguments necessary forinterpolation are passed through this object. Seeintamap-package for further description of the necessary content of this variable. |
... | other parameters for the generic method, not used for this method |
Details
Seepsgp-package andlearnParameters for further details.
Author(s)
Remi Barillec, Ben Ingram
See Also
learnParameters,estimateParameters,makePrediction,createIntamapObject
Examples
# load our favourite datasetdata(meuse)coordinates(meuse) = ~x+ymeuse$value = log(meuse$zinc)data(meuse.grid)gridded(meuse.grid) = ~x+yproj4string(meuse) = CRS("epsg:28992")proj4string(meuse.grid) = CRS("epsg:28992")# the following two steps are only needed if one wishes to# include observation errors# indicate which likelihood model should be used for each observation# in this case we use a different model for each observationnobs = length(meuse$value) # Number of observationsmeuse$oeid <- seq(1:nobs) # the variances for the error models are random in this example# in real examples they will come from actual measurements # characteristicsmeuse$oevar <- abs( rnorm( max(meuse$oeid) ) )# set up intamap object:obj = createIntamapObject( observations = meuse, predictionLocations = meuse.grid, targetCRS = "epsg:3035", class = "psgp" # Use PSGP for parameter estimation/interpolation)# do interpolation step:obj = conformProjections(obj)obj = estimateParameters(obj)Projected Sequential Gaussian Process
Description
learnParameters performs maximum likelihood parameter estimation in the PSGP framework.
Usage
learnParameters(object)Arguments
object | a list object of intamap type. Most arguments necessary forinterpolation are passed through this object. See |
Details
The Projected Spatial Gaussian Process (PSGP) framework provides an approximation to the full Gaussian process in which the observations are projected sequentially onto an optimal subset of 'active' observations. Spatial interpolation is done using a mixture of covariance kernels (exponential and Matern 5/2).
The functionlearnParameters is an internal function for estimating theparameters of the covariance function given the data, using a maximum likelihoodapproach. A valid intamapobject must be passed in.
PSGP is able to also take the measurement characteristics (i.e. errors) intoaccount using possibly many error models. For each error model, assumed Gaussian, the error variance can be specified. The vectorobject$observations$oevar contains all variances for the error models (one value per error model). Which error model is used for a given observation is determined by theobject$observations$oeid vector of indices, which specifies the index of the model to be used for each observation.
Warning
It is advised to use the intamap wrapperestimateParameters rather than calling this method directly.
Author(s)
Ben Ingram, Remi Barillec
References
Csato and Opper, 2002; Ingram et al., 2008
See Also
makePrediction,learnParameters,estimateParameters,createIntamapObject
Examples
# see example in estimateParametersSpatial projected sequential GP prediction
Description
makePrediction performs prediction/interpolation within the PSGP package.
Usage
makePrediction(object, vario)Arguments
object | a list object of intamap type. Most arguments necessary forinterpolation are passed through this object. Seeintamap-package for further description of the necessary content of this variable. Additional meta data about the measurement process is included in this object. In particular, seelearnParameters for a way to specify measurement error variances. |
vario | Log-parameters of the covariance function. For compatibility with the intamap package, the log-parameters of the PSGP covariance function are stored withina variogram array object (see |
Details
The Projected Spatial Gaussian Process (PSGP) framework provides an approximation to the full Gaussian process in which the observations are projected sequentially onto an optimal subset of 'active' observations. Spatial interpolation is done using a mixture of covariance kernels (Exponential and Matern 5/2).
The functionmakePrediction is a function for making predictions at a set of unobserved inputs (or locations).
Measurement characteristics (i.e. observation error) can be specified if needed. SeelearnParameters for a description of how to specify measurement errormodels with given variances.
Warning
It is advised to use the intamap wrapperspatialPredict rather than calling this method directly.
Author(s)
Ben Ingram, Remi Barillec
References
L. Csato and M. Opper. Sparse online Gaussian processes. Neural Computation, 14(3):641-669, 2002.
B. Ingram, D. Cornford, and D. Evans. Fast algorithms for automatic mapping with space-limited covariance functions. Stochastic Environmental Research and Risk Assessment, 22(5):661-670, 2008.
See Also
learnParametersspatialPredict,createIntamapObject
Examples
# see example in spatialPredictSpatial prediction using a Projected Sequential Gaussian Process (PSGP)
Description
This overloads thespatialPredict routine from the intamap package for interpolation using the PSGP method.
Usage
spatialPredict(object, ...)Arguments
object | a list object of type PSGP. Most arguments necessary for interpolation are passed through this object. See |
... | optional extra arguments (these are only used for debugging purposes) |
Details
Seepsgp-package andmakePrediction for further detail.
Author(s)
Ben Ingram, Remi Barillec
See Also
psgp-package,estimateParameters,makePredictioncreateIntamapObject
Examples
data(meuse)meuse = meuse[1:100,]coordinates(meuse) = ~x+ymeuse$value = log(meuse$zinc)data(meuse.grid)gridded(meuse.grid) = ~x+yproj4string(meuse) = CRS("epsg:28992")proj4string(meuse.grid) = CRS("epsg:28992")# Specify a different observation error model for each observation nobs = length(meuse$value) # Number of observationsmeuse$oeid = seq(1:nobs) # One error model per observation# Indicate the variance for each of these error modelsmeuse$oevar <- abs( rnorm( max(meuse$oeid) ) )# Set up intamap objectobj = createIntamapObject( observations = meuse, predictionLocations = meuse.grid, targetCRS = "epsg:3035", class = "psgp")# Estimate parameters and predict at new locations (interpolation)obj = conformProjections(obj)obj = estimateParameters(obj)obj = spatialPredict(obj)# Plot resultsplotIntamap(obj)