Update likelihoods_guide.py

docs/examples/likelihoods_guide.py

@@ -1,3 +1,4 @@
+# %% [markdown]
 # # Likelihood guide
 #
 # In this notebook, we will walk users through the process of creating a new likelihood
@@ -48,7 +49,7 @@
 # these methods in the forthcoming sections, but first, we will show how to instantiate
 # a likelihood object. To do this, we'll need a dataset.
 
-# +
+# %%
 # Enable Float64 for more stable matrix inversions.
 from jax import config
 
@@ -80,8 +81,8 @@
 ax.plot(x, y, "o", label="Observations")
 ax.plot(x, f(x), label="Latent function")
 ax.legend()
-# -
 
+# %% [markdown]
 # In this example, our observations have support $[-3, 3]$ and are generated from a
 # sinusoidal function with Gaussian noise. As such, our response values $\mathbf{y}$
 # range between $-1$ and $1$, subject to Gaussian noise. Due to this, a Gaussian
@@ -92,8 +93,10 @@
 # instantiating a likelihood object. We do this by specifying the `num_datapoints`
 # argument.
 
+# %%
 gpx.likelihoods.Gaussian(num_datapoints=D.n)
 
+# %% [markdown]
 # ### Likelihood parameters
 #
 # Some likelihoods, such as the Gaussian likelihood, contain parameters that we seek
@@ -105,8 +108,10 @@
 # initialise the likelihood standard deviation with a value of $0.5$, then we would do
 # this as follows:
 
+# %%
 gpx.likelihoods.Gaussian(num_datapoints=D.n, obs_stddev=0.5)
 
+# %% [markdown]
 # To control other properties of the observation noise such as trainability and value
 # constraints, see our [PyTree guide](pytrees.md).
 #
@@ -123,7 +128,7 @@
 # samples of $\mathbf{f}^{\star}$, whilst in red we see samples of
 # $\mathbf{y}^{\star}$.
 
-# +
+# %%
 kernel = gpx.kernels.Matern32()
 meanf = gpx.mean_functions.Zero()
 prior = gpx.gps.Prior(kernel=kernel, mean_function=meanf)
@@ -153,11 +158,11 @@
         color=cols[1],
         label="Predictive samples",
     )
-# -
 
+# %% [markdown]
 # Similarly, for a Bernoulli likelihood function, the samples of $y$ would be binary.
 
-# +
+# %%
 likelihood = gpx.likelihoods.Bernoulli(num_datapoints=D.n)
 
 
@@ -180,8 +185,8 @@
         color=cols[1],
         label="Predictive samples",
     )
-# -
 
+# %% [markdown]
 # ### Link functions
 #
 # In the above figure, we can see the latent samples being constrained to be either 0 or
@@ -229,7 +234,7 @@
 # this, let us consider a Gaussian likelihood where we'll first define a variational
 # approximation to the posterior.
 
-# +
+# %%
 z = jnp.linspace(-3.0, 3.0, 10).reshape(-1, 1)
 q = gpx.variational_families.VariationalGaussian(posterior=posterior, inducing_inputs=z)
 
@@ -240,27 +245,32 @@ def q_moments(x):
 
 
 mean, variance = jax.vmap(q_moments)(x[:, None])
-# -
 
+# %% [markdown]
 # Now that we have the variational mean and variational (co)variance, we can compute
 # the expected log-likelihood using the `expected_log_likelihood` method of the
 # likelihood object.
 
+# %%
 jnp.sum(likelihood.expected_log_likelihood(y=y, mean=mean, variance=variance))
 
+# %% [markdown]
 # However, had we wanted to do this using quadrature, then we would have done the
 # following:
 
+# %%
 lquad = gpx.likelihoods.Gaussian(
     num_datapoints=D.n,
     obs_stddev=jnp.array([0.1]),
-    integrator=gpx.integrators.GHQuadratureIntegrator(num_points=20),
 )
 
+# %% [markdown]
 # However, this is not recommended for the Gaussian likelihood given that the
 # expectation can be computed analytically.
 
+# %% [markdown]
 # ## System configuration
 
+# %%
 # %reload_ext watermark
 # %watermark -n -u -v -iv -w -a 'Thomas Pinder'