KernelFunctions.jl provides a flexible framework for defining kernel functions, and an extensive collection of implementations.
The aim is to make the API as model-agnostic as possible while still being user-friendly, and to interoperate well with generic packages for handling parameters like ParameterHandling.jl and FluxML's Functors.jl.
Where appropriate, kernels are AD-compatible.
x = range(-3.0, 3.0; length=100)
# A simple standardised squared-exponential / exponentiated-quadratic kernel.
k₁ = SqExponentialKernel()
K₁ = kernelmatrix(k₁, x)
# Set a function transformation on the data
k₂ = Matern32Kernel() ∘ FunctionTransform(sin)
K₂ = kernelmatrix(k₂, x)
# Set a matrix premultiplication on the data
k₃ = PolynomialKernel(; c=2.0, degree=2) ∘ LinearTransform(randn(4, 1))
K₃ = kernelmatrix(k₃, x)
# Add and sum kernels
k₄ = 0.5 * SqExponentialKernel() * LinearKernel(; c=0.5) + 0.4 * k₂
K₄ = kernelmatrix(k₄, x)
plot(
heatmap.([K₁, K₂, K₃, K₄]; yflip=true, colorbar=false)...;
layout=(2, 2), title=["K₁" "K₂" "K₃" "K₄"],
)
Directly inspired by the MLKernels package.
See the JuliaGaussianProcesses Github organisation and website for more related packages.
If you notice a problem or would like to contribute by adding more kernel functions or features please submit an issue, or open a PR (please see the ColPrac contribution guidelines).