gptk (version 1.06)

kernGradient: Compute the gradient wrt the kernel parameters.

Description

Compute the gradient wrt the kernel parameters.

Usage

kernGradient(kern, x, ...)
## kernGradient(kern, x, partial)
## kernGradient(kern, x, x1, x2, partial_)

Arguments

kern

the kernel structure for which the gradients are being computed.

x

the input locations for which the gradients are being computed.

...

other arguments such as: 'partial', a matrix of partial derivatives of the function of interest with respect to the kernel matrix. The argument takes the form of a square matrix of dimension numData, where numData is the number of rows in X,

Value

• g
  gradients of the function of interest with respect to the kernel parameters. The ordering of the vector should match that provided by the function kernExtractParam.

Details

g <- kernGradient(kern, x, partial) g <- *kernGradient(kern, x, partial) computes the gradient of functions with respect to the kernel parameters. As well as the kernel structure and the input positions, the user provides a matrix PARTIAL which gives the partial derivatives of the function with respect to the relevant elements of the kernel matrix.

g <- kernGradient(kern, x1, x2, partial_) g <- *kernGradient(kern, x1, x2, partial_) computes the derivatives as above, but input locations are now provided in two matrices associated with rows and columns of the kernel matrix.

g <- *X*kernGradient(kern1, kern2, x, partial) g <- *X*kernGradient(kern1, kern2, x1, x2, partial_) same as above, but for cross combinations of two kernels, kern1 and kern2.

See Also

kernCompute, kernExtractParam.

Examples

kern <- kernCreate(1, 'rbf')
g <- kernGradient(kern, as.matrix(c(1, 4)), array(1, c(2, 2)))