per: Periodic kernel

In goldingn/gpe: Gaussian Process Everything

Description

Construct a periodic kernel.

Usage

per(columns, p = 1, l = 1, sigma = 1)

Arguments

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.
p	a positive scalar parameter giving the periodicity of the kernel, the difference between values of the covariate at which period signal repeats
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.
sigma	a positive scalar parameter giving (the square-root of) the overall variance of the kernel

Details

The periodic kernel takes the form:

k_{per}(\mathbf{x}, \mathbf{x}') = σ^2 exp ≤ft(-\frac{2sin^2(π | \mathbf{x} - \mathbf{x}' | /p)}{l^2} \right)

where \mathbf{x} are the covariates on which the kernel is active, p determines the periodicity (distance between successive peaks), l is a characteristic lengthscale, as in the rbf kernel, and σ^2 is the amplitude of the signal

Value

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

See Also

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

Examples

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

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

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

goldingn/gpe documentation built on May 17, 2019, 7:41 a.m.