Evaluate a kernel specification — evaluate

The package offers two ways to compute a covariance matrix. Kernel specifications, such as rbf_kernel(), are objects: they can be combined with sum_kernel(), product_kernel(), and scale_kernel(), their parameters can be read, updated, and optimized, and models store them. evaluate_kernel() computes their covariance. The covariance functions, such as kernel_rbf(), take the parameter values as arguments and return one matrix directly. Both use the same formulas.

Usage

evaluate_kernel(kernel, x, y = NULL)

Arguments

kernel: A Gaussian-process kernel specification.
x: Numeric vector or matrix of observations.
y: Optional numeric vector or matrix. If NULL, evaluates the covariance of x with itself.

Value

A numeric covariance matrix.

Stability

Stable: from version 1.0.0 this interface changes incompatibly only in a major release, after a deprecation period. Results and options that concern an experimental model class, kernel, or argument follow that interface's tier. See gaussianprocesses-package for the policy.

Examples

kernel <- sum_kernel(rbf_kernel(length_scale = 0.5), white_noise_kernel(0.1))
x <- c(0, 0.5, 1)

evaluate_kernel(kernel, x)
#>           [,1]      [,2]      [,3]
#> [1,] 1.1000000 0.6065307 0.1353353
#> [2,] 0.6065307 1.1000000 0.6065307
#> [3,] 0.1353353 0.6065307 1.1000000

# Cross-covariance between training and new inputs.
evaluate_kernel(kernel, x, c(0.25, 2))
#>           [,1]         [,2]
#> [1,] 0.8824969 0.0003354626
#> [2,] 0.8824969 0.0111089965
#> [3,] 0.3246525 0.1353352832