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Clarify how to set up the lengthscale in the docs #212

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Update userguide.md
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26 changes: 16 additions & 10 deletions docs/src/userguide.md
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Expand Up @@ -7,14 +7,14 @@ For example to create a square exponential kernel
```julia
k = SqExponentialKernel()
```
Instead of having lengthscale(s) for each kernel we use `Transform` objects (see [Transform](@ref)) which are directly going to act on the inputs before passing them to the kernel.
For example to premultiply the input by 2.0 we create the kernel the following options are possible
!!! tip "How do I set the lengthscale?" Instead of having lengthscale(s) for each kernel we use `Transform` objects (see [Transform](@ref)) which are directly going to act on the inputs before passing them to the kernel.
For example, if you want to premultiply the input by 2.0, you can create your kernel with the following options:
```julia
k = transform(SqExponentialKernel(),ScaleTransform(2.0)) # returns a TransformedKernel
k = @kernel SqExponentialKernel() l=2.0 # Will be available soon
k = TransformedKernel(SqExponentialKernel(),ScaleTransform(2.0))
k = transform(SqExponentialKernel(), 2.0)) # returns a TransformedKernel
```
In the example of the [SqExponentialKernel](@ref), you can reproduce the usual definition, $$\exp\left(-\frac{\|x-x'\|^2}{\rho^2}\right)$$, by using `transform(SqExponentialKernel(), 1 / ρ)`.
Check the [`Transform`](@ref) page to see the other options.

To premultiply the kernel by a variance, you can use `*` or create a `ScaledKernel`
```julia
k = 3.0*SqExponentialKernel()
Expand Down Expand Up @@ -79,11 +79,17 @@ For example :

What if you want to differentiate through the kernel parameters? Even in a highly nested structure such as :
```julia
k = transform(0.5*SqExponentialKernel()*MaternKernel()+0.2*(transform(LinearKernel(),2.0)+PolynomialKernel()),[0.1,0.5])
k = transform(
0.5 * SqExponentialKernel() * MaternKernel()
+ 0.2 * (transform(LinearKernel(), 2.0) + PolynomialKernel()),
[0.1, 0.5])
```
One can get the array of parameters to optimize via `params` from `Flux.jl`

One can access the named tuple of trainable parameters via `Functors.functor` from `Functors.jl`.
This means that in practice you can implicitly optimize the kernel parameters by calling:
```julia
using Flux
params(k)
using Flux
kernelparams = Flux.params(k)
Flux.gradient(kernelparams) do
... some loss function on the kernel ....
end
```