SPGP-init: Sparse Gaussian Process
In italo-goncalves/geomod3D: Implicit 3D Geological Modeling and Geostatistics

Description Usage Arguments Details References See Also

Implementation of the Sparse Gaussian Process model for 3D spatial interpolation. Extends the GP class.

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SPGP(data, model, value, mean = NULL, trend = NULL, pseudo_inputs = data,
  force.interp = numeric(), reg.v = 1e-09, tangents = NULL,
  reg.t = 1e-12, pseudo_tangents = tangents, variational = T)

`data`	A `spatial3DDataFrame` object containing the data one wishes to model.
`model`	The covariance model. A `covarianceStructure3D` or a `list` containing one or more such objects.
`value`	The column name of the variable to be modeled. It is assumed the column does not contain missing values.
`mean`	The global mean. Irrelevant if a trend is provided.
`trend`	The model's trend component. A formula in character format.
`pseudo_inputs`	The desired number of pseudo-inputs (whose coordinates will be sampled from the data), a matrix or data frame with their coordinates, or a 3D object.
`force.interp`	Indices of points that must be interpolated exactly.
`reg.v`	Regularization to improve stability. A single value or a vector with length matching the number of data points.
`tangents`	A `directions3DDataFrame` object containing structural geology data. Most likely generated with the `GetLineDirections()` method.
`reg.t`	Regularization for structural data. A single value or a vector with length matching the number of structural data.
`pseudo_tangents`	The desired number of pseudo-structural data (whose coordinates will be sampled from the data) or a `directions3DDataFrame`.
`variational`	Use the variational approach?

This method builds a SPGP object with all the information needed to make preditions at new data points.

trend must be a character string with a formula as a function of uppercase X, Y, and Z. The most common is the linear trend, "~ X + Y + Z". For ordinary kriging, use "~1". If neither trend nor mean are given, it is assumed that the global mean is the mean of the data values.

The SPGP works by compressing the information coming from all data into a small number of pseudo-inputs. This way computational gains are obtained, but the resulting model may pose difficulties for training.

Given the sparse nature of the model, the points specified in force.interp may still not be interpolated exactly. The effects of tangent data may also be diminished.

The variational model is cited in the literature as more stable and less prone to overfitting. variational = F corresponds to the Fully Independent Conditional (FIC) approach.

Snelson, E., Ghahramani, Z., 2006. Sparse Gaussian Processes using Pseudo-inputs. Adv. Neural Inf. Process. Syst. 18 1257<e2><80><93>1264.

Titsias, M., 2009. Variational Learning of Inducing Variables in Sparse Gaussian Processes. Aistats 5, 567<e2><80><93>574.

Bauer, M.S., van der Wilk, M., Rasmussen, C.E., 2016. Understanding Probabilistic Sparse Gaussian Process Approximations. Adv. Neural Inf. Process. Syst. 29.

SPGP-class, GP-class

italo-goncalves/geomod3D documentation built on May 24, 2019, 2:49 p.m.