kernels | R Documentation |
Create and combine Gaussian process kernels (covariance functions) for use in Gaussian process models.
bias(variance)
constant(variance)
white(variance)
iid(variance, columns = 1)
rbf(lengthscales, variance, columns = seq_along(lengthscales))
rational_quadratic(
lengthscales,
variance,
alpha,
columns = seq_along(lengthscales)
)
linear(variances, columns = seq_along(variances))
polynomial(variances, offset, degree, columns = seq_along(variances))
expo(lengthscales, variance, columns = seq_along(lengthscales))
mat12(lengthscales, variance, columns = seq_along(lengthscales))
mat32(lengthscales, variance, columns = seq_along(lengthscales))
mat52(lengthscales, variance, columns = seq_along(lengthscales))
cosine(lengthscales, variance, columns = seq_along(lengthscales))
periodic(period, lengthscale, variance)
variance, variances |
(scalar/vector) the variance of a Gaussian process
prior in all dimensions ( |
columns |
(scalar/vector integer, not a greta array) the columns of the data matrix on which this kernel acts. Must have the same dimensions as lengthscale parameters. |
alpha |
(scalar) additional parameter in rational quadratic kernel |
offset |
(scalar) offset in polynomial kernel |
degree |
(scalar) degree of polynomial kernel |
period |
(scalar) the period of the Gaussian process |
lengthscale, lengthscales |
(scalar/vector) the correlation decay
distance along all dimensions ( |
The kernel constructor functions each return a function (of
class greta_kernel
) which can be executed on greta arrays to compute
the covariance matrix between points in the space of the Gaussian process.
The +
and *
operators can be used to combine kernel functions
to create new kernel functions.
Note that bias
and constant
are identical names for the same
underlying kernel.
iid
is equivalent to bias
where all entries in columns
match (where the absolute euclidean distance is less than
1e-12), and white
where they don't; i.e. an independent Gaussian
random effect.
greta kernel with class "greta_kernel"
## Not run:
# create a radial basis function kernel on two dimensions
k1 <- rbf(lengthscales = c(0.1, 0.2), variance = 0.6)
# evaluate it on a greta array to get the variance-covariance matrix
x <- greta_array(rnorm(8), dim = c(4, 2))
k1(x)
# non-symmetric covariance between two sets of points
x2 <- greta_array(rnorm(10), dim = c(5, 2))
k1(x, x2)
# create a bias kernel, with the variance as a variable
k2 <- bias(variance = lognormal(0, 1))
# combine two kernels and evaluate
K <- k1 + k2
K(x, x2)
# other kernels
constant(variance = lognormal(0, 1))
white(variance = lognormal(0, 1))
iid(variance = lognormal(0,1))
rational_quadratic(lengthscales = c(0.1, 0.2), alpha = 0.5, variance = 0.6)
linear(variances = 0.1)
polynomial(variances = 0.6, offset = 0.8, degree = 2)
expo(lengthscales = 0.6 ,variance = 0.9)
mat12(lengthscales = 0.5, variance = 0.7)
mat32(lengthscales = 0.4, variance = 0.8)
mat52(lengthscales = 0.3, variance = 0.9)
cosine(lengthscales = 0.68, variance = 0.8)
periodic(period = 0.71, lengthscale = 0.59, variance = 0.2)
## End(Not run)
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