gp_draw {gplite}

Make predictions with a GP model

Description

Function gp_pred can be used to make analytic predictions for the latent function values at test points, whereas gp_draw can be used to draw from the predictive distribution (or from the prior if the GP has not been fitted yet.)

Usage

gp_draw(
  gp,
  xnew,
  draws = NULL,
  transform = TRUE,
  target = FALSE,
  marginal = FALSE,
  cfind = NULL,
  jitter = NULL,
  seed = NULL,
  ...
)

gp_pred(
  gp,
  xnew,
  var = FALSE,
  quantiles = NULL,
  transform = FALSE,
  cfind = NULL,
  jitter = NULL,
  quad_order = 15,
  ...
)

Arguments

gp

A GP model object.

xnew

N-by-d matrix of input values (N is the number of test points and d the input dimension). Can also be a vector of length N if the model has only a single input.

draws

Number of draws to generate from the predictive distribution for the latent values.

transform

Whether to transform the draws of latent values to the same scale as the target y, that is, through the response (or inverse-link) function.

target

If TRUE, draws values for the target variable y instead of the latent function values.

marginal

If TRUE, then draws for each test point are only marginally correct, but the covariance structure between test points is not retained. However, this will make the sampling considerably faster in some cases, and can be useful if one is interested only in looking at the marginal predictive distributions for a large number of test locations (for example, in posterior predictive checking).

cfind

Indices of covariance functions to be used in the prediction. By default uses all covariance functions.

jitter

Magnitude of diagonal jitter for covariance matrices for numerical stability. Default is 1e-6.

seed

Random seed for draws.

...

Additional parameters that might be needed. For example offset or keyword trials for binomial and beta-binomial likelihoods.

var

Whether to compute the predictive variances along with predictive mean.

quantiles

Vector of probabilities between 0 and 1 indicating which quantiles are to be predicted.

quad_order

Quadrature order in order to compute the mean and variance on the transformed scale.

Value

gp_pred returns a list with fields giving the predictive mean, variance and quantiles (the last two are computed only if requested). gp_draw returns an N-by-draws matrix of random draws from the predictive distribution, where N is the number of test points.

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])

# More than one covariance function; one for x1 and x2, and another one for x3
cf1 <- cf_nn(c("x1", "x2"), prior_sigma0 = prior_half_t(df = 4, scale = 2))
cf2 <- cf_sexp("x3")
cfs <- list(cf1, cf2)
lik <- lik_gaussian()
gp <- gp_init(cfs, lik)
gp <- gp_optim(gp, x, y, maxiter = 500)

# plot the predictions with respect to x1, when x2 = x3 = 0
xt <- cbind(x1 = seq(-3, 3, len = 50), x2 = 0, x3 = 0)
pred <- gp_pred(gp, xt)
plot(xt[, "x1"], pred$mean, type = "l")

# draw from the predictive distribution
xt <- cbind(x1 = seq(-3, 3, len = 50), x2 = 0, x3 = 0)
draws <- gp_draw(gp, xt, draws = 100)
plot(xt[, "x1"], draws[, 1], type = "l")
for (i in 2:50) {
  lines(xt[, "x1"], draws[, i])
}

# plot effect with respect to x3 only
xt <- cbind("x3" = seq(-3, 3, len = 50))
pred <- gp_pred(gp, xt, cfind = 2)
plot(xt, pred$mean, type = "l")