rq: Rational quadratic kernel
In goldingn/gpe: Gaussian Process Everything

Description Usage Arguments Details Value See Also Examples

Construct a rational quadratic kernel.

1	rq(columns, sigma = 1, l = rep(1, length(columns)), alpha = 1)

`columns`	a string vector giving the names of features on which the kernel acts. These will be used to access columns from a dataframe when the kernel is later used in a GP model.
`sigma`	a positive scalar parameter giving (the square-root of) the overall variance of the kernel
`l`	a positive scalar or vector parameter giving the characteristic lengthscale of the kernel (how rapidly the covariance decays with difference in the value of the covariate). Larger values of `l` imply less complex functions.
`alpha`	a positive scalar or vector parameter controlling the roughness of the GPs drawn from the kernel. Larger values of `alpha` imply rougher complex functions.

The rational quadratic kernel takes the form:

k_{rq}(\mathbf{x}, \mathbf{x}') = σ^2 ≤ft(1 + \frac{\mathbf{r} ^ 2}{α} \right) ^ {-α}

\mathbf{r} = {√{∑\limits_{d=1}^D ≤ft(\frac{(x_d - x_d')}{2l_d^2}\right) ^ 2}}

where \mathbf{x} are the covariates on which the kernel is active, l_d are the characteristic lengthscales for each covariate (column) x_d, σ^2 is the overall variance and α controls the roughness.

Larger values of l_i correspond to functions in which change less rapidly over the values of the covariates.

A kernel object for which there are a range of associated functions, see kernel and access for details.

Other kernel.constructors: composition, expo, iid, int, lin, mat32, mat52, per, rbf

# construct a kernel with one feature
k1 <- rq('temperature')

# and another with two features
k2 <- rq(c('temperature', 'pressure'))

# evaluate them on the pressure dataset
image(k1(pressure))
image(k2(pressure))