SLGP (version 1.0.1)

slgp: Define and can train a Spatial Logistic Gaussian Process (SLGP) model

Description

This function builds and trains an SLGP model based on a specified formula and data. The SLGP is a finite-rank Gaussian process model for conditional density estimation, trained using MAP, MCMC, Laplace approximation, or left untrained ("none").

Usage

slgp(
  formula,
  data,
  epsilonStart = NULL,
  method,
  basisFunctionsUsed,
  interpolateBasisFun = "NN",
  nIntegral = 101,
  nDiscret = 101,
  hyperparams = NULL,
  predictorsUpper = NULL,
  predictorsLower = NULL,
  responseRange = NULL,
  sigmaEstimationMethod = "none",
  seed = NULL,
  opts_BasisFun = list(),
  BasisFunParam = NULL,
  opts = list(),
  trend = NULL,
  verbose = FALSE
)

Value

An object of S4 class SLGP-class, containing:

coefficients

Matrix of posterior (or prior) draws of the SLGP coefficients \(\epsilon_i\).

hyperparams

List of fitted or provided hyperparameters.

logPost

Log-posterior (if MAP or Laplace used).

method

Estimation method used.

...

Other internal information such as ranges, basis settings, and data.

Arguments

formula

A formula specifying the model structure, with the response on the left-hand side and covariates on the right.

data

A data frame containing the variables used in the formula.

epsilonStart

Optional numeric vector of initial weights for the finite-rank GP: \(Z(x,t) = \sum_{i=1}^p \epsilon_i f_i(x, t)\).

method

Character string specifying the training method: one of {"none", "MCMC", "MAP", "Laplace"}.

basisFunctionsUsed

Character string describing the basis function type: one of "inducing points", "RFF", "Discrete FF", "filling FF", or "custom cosines".

interpolateBasisFun

Character string indicating how to evaluate basis functions: "nothing" (exact eval), "NN" (nearest-neighbor), or "WNN" (weighted inverse-distance). Default is "NN".

nIntegral

Number of quadrature points used for numerical integration over the response domain.

nDiscret

Integer controlling the resolution of the interpolation grid (used only for "NN" or "WNN").

hyperparams

Optional list of hyperparameters. Should contain:

• sigma2: signal variance

• lengthscale: vector of lengthscales (one per covariate)

predictorsUpper

Optional numeric vector for the upper bounds of the covariates (used for scaling).

predictorsLower

Optional numeric vector for the lower bounds of the covariates.

responseRange

Optional numeric vector of length 2 with the lower and upper bounds of the response.

sigmaEstimationMethod

Method to heuristically estimate the variance sigma2. Either "none" (default) or "heuristic".

seed

Optional integer for reproducibility.

opts_BasisFun

List of optional configuration parameters passed to the basis function initializer.

BasisFunParam

Optional list of precomputed basis function parameters.

opts

Optional list of extra settings passed to inference routines (e.g., stan_iter, stan_chains, ndraws).

trend

Optional a function that returns the trend of the transformed GP (not to be estimated). If not provided, it defaults to 0.

verbose

Logical; if TRUE, print progress and diagnostic messages during computation. Defaults to FALSE.

References

Gautier, Athénaïs (2023). "Modelling and Predicting Distribution-Valued Fields with Applications to Inversion Under Uncertainty." Thesis, Universität Bern, Bern. https://boristheses.unibe.ch/4377/

Examples

# \donttest{
# Load Boston housing dataset
library(MASS)
data("Boston")
# Set input and output ranges manually (you can also use range(Boston$age), etc.)
range_x <- c(0, 100)
range_response <- c(0, 50)

#' #Create a SLGP model but don't fit it
modelPrior <- slgp(medv ~ age,        # Use a formula to specify response and covariates
                 data = Boston,     # Use the original Boston housing data
                 method = "none",    # No training
                 basisFunctionsUsed = "RFF",         # Random Fourier Features
                 sigmaEstimationMethod = "heuristic",  # Auto-tune sigma2 (more stable)
                 predictorsLower = range_x[1],         # Lower bound for 'age'
                 predictorsUpper = range_x[2],         # Upper bound for 'age'
                 responseRange = range_response,       # Range for 'medv'
                 opts_BasisFun = list(nFreq = 200,     # Use 200 Fourier features
                                      MatParam = 5/2), # Matern 5/2 kernel
                 seed = 1)                             # Reproducibility

# Train an SLGP model using MAP estimation and RFF basis
modelMAP <- slgp(medv ~ age,        # Use a formula to specify response and covariates
                 data = Boston,     # Use the original Boston housing data
                 method = "MAP",    # Train using Maximum A Posteriori estimation
                 basisFunctionsUsed = "RFF",         # Random Fourier Features
                 sigmaEstimationMethod = "heuristic",  # Auto-tune sigma2 (more stable)
                 predictorsLower = range_x[1],         # Lower bound for 'age'
                 predictorsUpper = range_x[2],         # Upper bound for 'age'
                 responseRange = range_response,       # Range for 'medv'
                 opts_BasisFun = list(nFreq = 200,     # Use 200 Fourier features
                                      MatParam = 5/2),  # Matern 5/2 kernel
                 seed = 1)                             # Reproducibility
# }