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Extend lengthscale tip #476

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Merged
merged 5 commits into from
Sep 26, 2022
Merged

Extend lengthscale tip #476

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ad05748
Extend lengthscale tip
Sep 26, 2022
d5bd514
Tweak docstring
Sep 26, 2022
b36f83b
Merge branch 'master' into wct/docs-improvement
willtebbutt Sep 26, 2022
ac608a0
Pluralise title of tip
Sep 26, 2022
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Merge in master'
Sep 26, 2022
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13 changes: 13 additions & 0 deletions docs/src/userguide.md
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Expand Up @@ -21,6 +21,19 @@ For example, a squared exponential kernel is created by
```
[`with_lengthscale`](@ref) also works with vector-valued lengthscales for ARD.
Check the [Input Transforms](@ref input_transforms) page for more details.
Per-dimension lengthscales for automatic relevance determination work in a similar manner:
```julia
inverse_length_scales = [1.0, 2.0]
k = SqExponentialKernel() ∘ ARDTransform(inverse_length_scales)
k = compose(SqExponentialKernel(), ARDTransform(inverse_length_scales))
```
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I thought commonly one would just use with_lengthscale? ARD is actually mentioned two lines above 🙂

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Huh. I hadn't realised that is a thing! Maybe I should just add an example with a vector of lengthscales to the tip then, rather than extending substantially? And maybe change the title to "How do I set the lengthscale(s)?"?

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I think these are good suggestions.

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Have tweaked -- let me know if you think it works.

More generally, you can utilise arbitrary matrices via [`LinearTransform`](@ref).
For example, this can be used to project inputs from high- to low- dimensions:
```julia
A = randn(1, 2)
k = compose(SqExponentialKernel(), LinearTransform(A))
```
In this case, we map from `2` to `1` dimension.

!!! tip "How do I set the kernel variance?"
To premultiply the kernel by a variance, you can use `*` with a scalar number:
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