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KernelFunctions.jl is a general purposekernel package.It provides a flexible framework for creating kernel functions and manipulating them, and an extensive collection of implementations.The main goals of this package are:

• Flexibility: operations between kernels should be fluid and easy without breaking, with a user-friendly API.
• Plug-and-play: being model-agnostic; including the kernels before/after other steps should be straightforward. To interoperate well with generic packages for handling parameters likeParameterHandling.jl and FluxML'sFunctors.jl.
• Automatic Differentiation compatibility: all kernel functions whichought to be differentiable using AD packages likeForwardDiff.jl orZygote.jlshould be.

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 datak₂=Matern32Kernel()∘FunctionTransform(sin)K₂=kernelmatrix(k₂, x)# Set a matrix premultiplication on the datak₃=PolynomialKernel(; c=2.0, degree=2)∘LinearTransform(randn(4,1))K₃=kernelmatrix(k₃, x)# Add and sum kernelsk₄=0.5*SqExponentialKernel()*LinearKernel(; c=0.5)+0.4* k₂K₄=kernelmatrix(k₄, x)plot(heatmap.([K₁, K₂, K₃, K₄]; yflip=true, colorbar=false)...;    layout=(2,2), title=["K₁""K₂""K₃""K₄"],)

This package replaces the now-defunctMLKernels.jl. It incorporates lots of excellent existing work from packages such asGaussianProcesses.jl, and is used in downstream packages such asAbstractGPs.jl,ApproximateGPs.jl,Stheno.jl, andAugmentedGaussianProcesses.jl.

See the JuliaGaussianProcessesGithub organisation andwebsite for more information.

If you notice a problem or would like to contribute by adding more kernel functions or features pleasesubmit an issue, or open a PR (please see theColPrac contribution guidelines).