GLOM Kernel Creation

GLOM requires latent GP kernels that are at least twice mean-square differentiable in order to ensure that second order derivatives exist for non-trivial model construction. All of the derived versions of the kernels that are necessary can be created using the following function.

GPLinearODEMaker.include_lag_kernel — Method

include_lag_kernel(kernel_name)

Provides a kernel for modelling two variables with the same shared latent GP, but with a lag term between them using one of GLOM's base kernels. The returned kernel function should be called with the lag hyperparameter appended to the end of the hyperparameters for the base kernel.

Arguments

kernel_name::String: The base kernel function to use. Passed to includekernel(kernelname)

source

GPLinearODEMaker.kernel_coder — Method

kernel_coder(symbolic_kernel_original, kernel_name; periodic_var="", cutoff_var="", loc="src/kernels/")

Creates the necessary differentiated versions of base kernels required by GLOM and saves the script containing them to loc

Arguments

symbolic_kernel_original::Basic: Kernel function created using variables declared with SymEngine's @vars macro
kernel_name::String: The name the kernel function will be saved with
periodic_var::String="": If changed, tries to convert the named variable (currently only one) into a periodic variable by replacing it with 2*sin(π*δ/periodic_var)
cutoff_var::String="": If changed, makes the kernel return 0 for abs(δ) > cutoff_var
loc::String="src/kernels/": The location where the script will be saved

Extra Info

The created function will look like this

$kernel_name(hyperparameters::Vector{<:Real}, δ::Real; dorder::Vector{<:Integer}=zeros(Int64, length(hyperparameters) + 2))

For example, you could define a kernel like so:

"Radial basis function GP kernel (aka squared exonential, ~gaussian)"
function se_kernel_base(λ::Number, δ::Number)
    return exp(-δ ^ 2 / (2 * λ ^ 2))
end

And then calculate the necessary derivative versions like so:

@vars δ λ
kernel_coder(se_kernel_base(λ, δ), "se")

The function is saved in loc * kernel_name * "_kernel.jl", so you can use it with a command akin to this:

include(loc * kernel_name * "_kernel.jl")