Add BO notebook

Added introduction to Bayesian optimisation notebook. Also fixed some links which had broken after renaming the old kernels notebook in a previous PR.
JaxGaussianProcesses · Jul 14, 2023 · 5375ae4 · 5375ae4
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diff --git a/README.md b/README.md
@@ -54,7 +54,7 @@ process modelling.
 > - [**Stochastic Variational Inference**](https://docs.jaxgaussianprocesses.com/examples/uncollapsed_vi/)
 > - [**BlackJax Integration**](https://docs.jaxgaussianprocesses.com/examples/classification/#mcmc-inference)
 > - [**Laplace Approximation**](https://docs.jaxgaussianprocesses.com/examples/classification/#laplace-approximation)
-> - [**Inference on Non-Euclidean Spaces**](https://docs.jaxgaussianprocesses.com/examples/kernels/#custom-kernel)
+> - [**Inference on Non-Euclidean Spaces**](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels/#custom-kernel)
 > - [**Inference on Graphs**](https://docs.jaxgaussianprocesses.com/examples/graph_kernels/)
 > - [**Pathwise Sampling**](https://docs.jaxgaussianprocesses.com/examples/spatial/)
 > - [**Learning Gaussian Process Barycentres**](https://docs.jaxgaussianprocesses.com/examples/barycentres/)
@@ -63,7 +63,7 @@ process modelling.
 
 ## Guides for customisation
 >
-> - [**Custom kernels**](https://docs.jaxgaussianprocesses.com/examples/kernels/#custom-kernel)
+> - [**Custom kernels**](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels/#custom-kernel)
 > - [**UCI regression**](https://docs.jaxgaussianprocesses.com/examples/yacht/)
 
 ## Conversion between `.ipynb` and `.py`

diff --git a/docs/examples/barycentres.py b/docs/examples/barycentres.py
@@ -124,7 +124,7 @@
 # optimised. For advice on achieving this, see the
 # [Regression notebook](https://docs.jaxgaussianprocesses.com/examples/regression/)
 # for advice on optimisation and the
-# [Kernels notebook](https://docs.jaxgaussianprocesses.com/examples/kernels/) for
+# [Kernels notebook](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels/) for
 # advice on selecting an appropriate kernel.
 
 

diff --git a/docs/examples/bayesian_optimisation.py b/docs/examples/bayesian_optimisation.py
diff --git a/docs/examples/deep_kernels.py b/docs/examples/deep_kernels.py
@@ -130,7 +130,7 @@ def __call__(
 # activation functions between the layers. The first hidden layer contains 64 units,
 # while the second layer contains 32 units. Finally, we'll make the output of our
 # network a three units wide. The corresponding kernel that we define will then be of
-# [ARD form](https://docs.jaxgaussianprocesses.com/examples/kernels/#active-dimensions)
+# [ARD form](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels/#active-dimensions)
 # to allow for different lengthscales in each dimension of the feature space.
 # Users may wish to design more intricate network structures for more complex tasks,
 # which functionality is supported well in Haiku.

diff --git a/docs/examples/graph_kernels.py b/docs/examples/graph_kernels.py
@@ -5,7 +5,7 @@
 # of a graph using a Gaussian process with a Matérn kernel presented in
 # <strong data-cite="borovitskiy2021matern"></strong>. For a general discussion of the
 # kernels supported within GPJax, see the
-# [kernels notebook](https://docs.jaxgaussianprocesses.com/examples/kernels).
+# [kernels notebook](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels).
 
 # %%
 # Enable Float64 for more stable matrix inversions.

diff --git a/docs/examples/intro_to_gps.py b/docs/examples/intro_to_gps.py
@@ -447,8 +447,8 @@
 # that are admissible under the GP prior. A kernel is a positive-definite
 # function with parameters $\boldsymbol{\theta}$ that maps pairs of inputs
 # $\mathbf{X}, \mathbf{X}' \in \mathcal{X}$ onto the real line. We dedicate the
-# entirety of the [Kernel Guide
-# notebook](https://docs.jaxgaussianprocesses.com/examples/kernels) to
+# entirety of the [Introduction to Kernels
+# notebook](https://docs.jaxgaussianprocesses.com/examples/intro_to_kernels) to
 # exploring the different GPs each kernel can yield.
 #
 # ## Gaussian process regression

diff --git a/docs/examples/intro_to_kernels.py b/docs/examples/intro_to_kernels.py
@@ -212,11 +212,11 @@ def forrester(x: Float[Array, "N"]) -> Float[Array, "N"]:
 test_y = forrester(test_x)
 
 # %% [markdown]
-# First we define our model, using the Matérn32 kernel, and construct our posterior *without* optimising the kernel hyperparameters:
+# First we define our model, using the Matérn52 kernel, and construct our posterior *without* optimising the kernel hyperparameters:
 
 # %%
 mean = gpx.mean_functions.Zero()
-kernel = gpx.kernels.Matern32(
+kernel = gpx.kernels.Matern52(
     lengthscale=jnp.array(2.0)
 )  # Initialise our kernel lengthscale to 2.0
 
@@ -672,7 +672,7 @@ def forrester(x: Float[Array, "N"]) -> Float[Array, "N"]:
 #
 # - [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/RW.pdf) - Chapter 4 provides a comprehensive overview of kernels, diving deep into some of the technical details and also providing some kernels defined on non-Euclidean spaces such as strings.
 # - David Duvenaud's [Kernel Cookbook](https://www.cs.toronto.edu/~duvenaud/cookbook/) is a great resource for learning about kernels, and also provides some information about some of the pitfalls people commonly encounter when using the Matérn family of kernels. His PhD thesis, [Automatic Model Construction with Gaussian Processes](https://www.cs.toronto.edu/~duvenaud/thesis.pdf), also provides some in-depth recipes for how one may incorporate their prior knowledge when constructing kernels.
-# - Finally, please check out our [more advanced kernel guide](https://docs.jaxgaussianprocesses.com/examples/kernels/), which details some more kernels available in GPJax as well as how one may combine kernels together to form more complex kernels.
+# - Finally, please check out our [more advanced kernel guide](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels/), which details some more kernels available in GPJax as well as how one may combine kernels together to form more complex kernels.
 #
 # ## System Configuration
 

diff --git a/docs/examples/spatial.py b/docs/examples/spatial.py
@@ -133,7 +133,7 @@
 # alone isn't enough to to a decent job at interpolating this data. Therefore, we can also use elevation and optimize
 # the parameters of our kernel such that more relevance should be given to elevation. This is possible by using a
 # kernel that has one length-scale parameter per input dimension: an automatic relevance determination (ARD) kernel.
-# See our [kernel notebook](https://docs.jaxgaussianprocesses.com/examples/kernels/) for more an introduction to
+# See our [kernel notebook](https://docs.jaxgaussianprocesses.com/examples/constructing_new_kernels/) for more an introduction to
 # kernels in GPJax.
 
 # %%

diff --git a/mkdocs.yml b/mkdocs.yml
@@ -28,6 +28,7 @@ nav:
     - Sparse GPs: examples/uncollapsed_vi.py
     - Stochastic sparse GPs: examples/collapsed_vi.py
     - Pathwise Sampling for Spatial Modelling: examples/spatial.py
+    - Bayesian Optimisation: examples/bayesian_optimisation.py
   - 📖 Guides for customisation:
     - Kernels: examples/constructing_new_kernels.py
     - Likelihoods: examples/likelihoods_guide.py