Gaussian processes in greta
greta.gp extends greta to let you define Gaussian
processes as part of your model. It provides a syntax to create and
combine GP kernels, and use them to define either full rank or sparse
Gaussian processes.
Example
# simulate data
x <- runif(20, 0, 10)
y <- sin(x) + rnorm(20, 0, 0.5)
x_plot <- seq(-1, 11, length.out = 200)library(greta)
library(greta.gp)
# hyperparameters
rbf_var <- lognormal(0, 1)
rbf_len <- lognormal(0, 1)
obs_sd <- lognormal(0, 1)
# kernel & GP
kernel <- rbf(rbf_len, rbf_var) + bias(1)
f <- gp(x, kernel)
# likelihood
distribution(y) <- normal(f, obs_sd)
# prediction
f_plot <- project(f, x_plot)# fit the model by Hamiltonian Monte Carlo
m <- model(f_plot)
draws <- mcmc(m)# plot 200 posterior samples
plot(
y ~ x,
pch = 16,
col = grey(0.4),
xlim = c(0, 10),
ylim = c(-2.5, 2.5),
las = 1,
fg = grey(0.7),
)
for (i in 1:200) {
lines(
draws[[1]][i, ] ~ x_plot,
lwd = 2,
col = rgb(0.7, 0.1, 0.4, 0.1)
)
}