cf: Initialize covariance function

In gplite: General Purpose Gaussian Process Modelling

Initialize covariance function

Description

Functions for initializing the covariance functions which can then be passed to gp_init. See section Details for explanation of what covariance function is what.

Usage

cf_const(magn = 1, prior_magn = prior_logunif())

cf_lin(vars = NULL, magn = 1, prior_magn = prior_logunif(), normalize = FALSE)

cf_sexp(
  vars = NULL,
  lscale = 0.3,
  magn = 1,
  prior_lscale = prior_logunif(),
  prior_magn = prior_logunif(),
  normalize = FALSE
)

cf_matern32(
  vars = NULL,
  lscale = 0.3,
  magn = 1,
  prior_lscale = prior_logunif(),
  prior_magn = prior_logunif(),
  normalize = FALSE
)

cf_matern52(
  vars = NULL,
  lscale = 0.3,
  magn = 1,
  prior_lscale = prior_logunif(),
  prior_magn = prior_logunif(),
  normalize = FALSE
)

cf_nn(
  vars = NULL,
  sigma0 = 1,
  sigma = 3,
  magn = 1,
  prior_sigma0 = prior_half_t(),
  prior_sigma = prior_half_t(),
  prior_magn = prior_logunif(),
  normalize = TRUE
)

cf_periodic(
  vars = NULL,
  period = 1,
  cf_base = cf_sexp(),
  prior_period = prior_logunif()
)

cf_prod(...)

## S3 method for class 'cf'
cf1 * cf2

Arguments

magn	Initial value for the magnitude hyperparameter (depicts the magnitude of the variation captured by the given covariance function).
prior_magn	Prior for hypeparameter magn. See priors.
vars	Indices of the inputs which are taken into account when calculating this covariance. If the input matrix has named columns, can also be a vector of column names. Default is all the inputs.
normalize	Whether to automatically scale and center the inputs for the given covariance function. Can be useful for inputs with mean and variance far from 0 and 1, respectively.
lscale	Initial value for the length-scale hyperparameter.
prior_lscale	Prior for hyperparameter lscale. See priors.
sigma0	Prior std for the bias in the neural network covariance function.
sigma	Prior std for the weights in the hidden layers of the neural network covariance function.
prior_sigma0	Prior for hyperparameter sigma0. See priors.
prior_sigma	Prior for hyperparameter sigma. See priors.
period	Period length for the periodic covariance function.
cf_base	Base covariance function that is used to model the variability within each period in periodic covariance function.
prior_period	Prior for hyperparameter period. See priors.
...	Meaning depends on context. For cf_prod pass in the covariance functions in the product.
cf1	Instance of a covariance function.
cf2	Instance of a covariance function.

Details

The supported covariance functions are (see Rasmussen and Williams, 2006):

cf_const

Constant covariance function. Can be used to model the intercept.

cf_lin

Linear covariance function. Produces linear functions.

cf_sexp

Squared exponential (or exponentiated quadratic, or Gaussian) covariance function.

cf_matern32

Matern nu=3/2 covariance function.

cf_matern52

Matern nu=5/2 covariance function.

cf_nn

Neural network covariance function.

cf_periodic

Periodic covariance function. The periodicity is achieved by mapping the original inputs through sine and cosine functions, and then applying the base kernel in this new space.

cf_prod

Product of two or more covariance functions.

Value

The covariance function object.

References

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.

Examples

# Generate some toy data
set.seed(1242)
n <- 50
x <- matrix(rnorm(n * 3), nrow = n)
f <- sin(x[, 1]) + 0.5 * x[, 2]^2 + x[, 3]
y <- f + 0.5 * rnorm(n)
x <- data.frame(x1 = x[, 1], x2 = x[, 2], x3 = x[, 3])

# Basic usage (single covariance function)
cf <- cf_sexp()
lik <- lik_gaussian()
gp <- gp_init(cf, lik)
gp <- gp_optim(gp, x, y)
plot(gp_pred(gp, x)$mean, y)

# More than one covariance function; one for x1 and x2, and another one for x3
cf1 <- cf_sexp(c("x1", "x2"))
cf2 <- cf_lin("x3")
cfs <- list(cf1, cf2)
lik <- lik_gaussian()
gp <- gp_init(cfs, lik)
gp <- gp_optim(gp, x, y, maxiter = 500)
plot(gp_pred(gp, x)$mean, y)
plot(x[, 3], gp_pred(gp, x, cfind = 2)$mean) # plot effect w.r.t x3 only

gplite documentation built on Aug. 24, 2022, 9:07 a.m.