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

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18 changes: 11 additions & 7 deletions docs/src/userguide.md
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Expand Up @@ -7,14 +7,15 @@ 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
k = TransformedKernel(SqExponentialKernel(), ScaleTransform(2.0))
```
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 @@ -79,9 +80,12 @@ 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 array of trainable parameters via `params` from `Flux.jl`

```julia
using Flux
Expand Down