Move params to the first slot of each function, class, etc.

README.md

@@ -89,7 +89,7 @@ posterior = prior * likelihood
 Equipped with the posterior, we seek to learn the model's hyperparameters through gradient-optimisation of the marginal log-likelihood. We this below, adding Jax's [just-in-time (JIT)](https://jax.readthedocs.io/en/latest/jax-101/02-jitting.html) compilation to accelerate training. 
 
 ```python
-mll = jit(posterior.marginal_log_likelihood(training, negative=True))
+mll = jit(posterior.marginal_log_likelihood(D, negative=True))
 ```
 
 For purposes of optimisation, we'll use optax's Adam.
@@ -117,11 +117,11 @@ Using our learned hyperparameters, we can obtain the posterior distribution of t
 learned_params, _ = inference_state.unpack()
 xtest = jnp.linspace(-3., 3., 100).reshape(-1, 1)
 
-latent_distribution = posterior(training, learned_params)(xtest)
-predictive_distribution = likelihood(latent_distribution, params)
+latent_distribution = posterior(learned_params, D)(xtest)
+predictive_distribution = likelihood(params, latent_distribution)
 
 predictive_mean = predictive_distribution.mean
-predictive_cov = predictive_distribution.covariance_matrix
+predictive_cov = predictive_distribution.covariance
 ```
 
 # Installation

examples/barycentres.pct.py

@@ -117,7 +117,7 @@ def fit_gp(x: jnp.DeviceArray, y: jnp.DeviceArray) -> dx.MultivariateNormalTri:
     )
 
     learned_params, training_history = inference_state.unpack()
-    return likelihood(posterior(D, learned_params)(xtest), learned_params)
+    return likelihood(learned_params, posterior(learned_params, D)(xtest))
 
 
 posterior_preds = [fit_gp(x, i) for i in ys]

examples/classification.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -98,9 +98,9 @@
 # From which we can make predictions at novel inputs, as illustrated below.
 
 # %%
-map_latent_dist = posterior(D, map_estimate)(xtest)
+map_latent_dist = posterior(map_estimate, D)(xtest)
 
-predictive_dist = likelihood(map_latent_dist, map_estimate)
+predictive_dist = likelihood(map_estimate, map_latent_dist)
 
 predictive_mean = predictive_dist.mean()
 predictive_std = predictive_dist.stddev()
@@ -159,11 +159,11 @@
 # that we identify as a Gaussian distribution,  $p(\boldsymbol{f}| \mathcal{D}) \approx q(\boldsymbol{f}) := \mathcal{N}(\hat{\boldsymbol{f}}, [-\nabla^2 \tilde{p}(\boldsymbol{y}|\boldsymbol{f})|_{\hat{\boldsymbol{f}}} ]^{-1} )$. Since the negative Hessian is positive definite, we can use the Cholesky decomposition to obtain the covariance matrix of the Laplace approximation at the datapoints below.
 
 # %%
-gram, cross_covariance = (prior.kernel.gram, prior.kernel.cross_covariance)
+gram, cross_covariance = (kernel.gram, kernel.cross_covariance)
 jitter = 1e-6
 
 # Compute (latent) function value map estimates at training points:
-Kxx = gram(prior.kernel, x, map_estimate["kernel"])
+Kxx = gram(kernel, map_estimate["kernel"], x)
 Kxx += I(D.n) * jitter
 Lx = Kxx.triangular_lower()
 f_hat = jnp.matmul(Lx, map_estimate["latent"])
@@ -193,10 +193,10 @@
 # %%
 def construct_laplace(test_inputs: Float[Array, "N D"]) -> dx.MultivariateNormalTri:
 
-    map_latent_dist = posterior(D, map_estimate)(test_inputs)
+    map_latent_dist = posterior(map_estimate, D)(test_inputs)
 
-    Kxt = cross_covariance(prior.kernel, x, test_inputs, map_estimate["kernel"])
-    Kxx = gram(prior.kernel, x, map_estimate["kernel"])
+    Kxt = cross_covariance(kernel, map_estimate["kernel"], x, test_inputs)
+    Kxx = gram(kernel, map_estimate["kernel"], x)
     Kxx += I(D.n) * jitter
     Lx = Kxx.triangular_lower()
 
@@ -219,7 +219,7 @@ def construct_laplace(test_inputs: Float[Array, "N D"]) -> dx.MultivariateNormal
 # From this we can construct the predictive distribution at the test points.
 # %%
 laplace_latent_dist = construct_laplace(xtest)
-predictive_dist = likelihood(laplace_latent_dist, map_estimate)
+predictive_dist = likelihood(map_estimate, laplace_latent_dist)
 
 predictive_mean = predictive_dist.mean()
 predictive_std = predictive_dist.stddev()
@@ -338,8 +338,8 @@ def one_step(state, rng_key):
     ps["latent"] = states.position["latent"][i, :, :]
     ps = gpx.constrain(ps, bijectors)
 
-    latent_dist = posterior(D, ps)(xtest)
-    predictive_dist = likelihood(latent_dist, ps)
+    latent_dist = posterior(ps, D)(xtest)
+    predictive_dist = likelihood(ps, latent_dist)
     samples.append(predictive_dist.sample(seed=key, sample_shape=(10,)))
 
 samples = jnp.vstack(samples)

examples/collapsed_vi.pct.py

@@ -8,7 +8,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -101,7 +101,7 @@
 
 negative_elbo = jit(sgpr.elbo(D, negative=True))
 
-optimiser = ox.adam(learning_rate=0.005)
+optimiser = ox.adam(learning_rate=5e-3)
 
 inference_state = gpx.fit(
     objective=negative_elbo,
@@ -116,8 +116,8 @@
 # We show predictions of our model with the learned inducing points overlayed in grey.
 
 # %%
-latent_dist = q.predict(D, learned_params)(xtest)
-predictive_dist = likelihood(latent_dist, learned_params)
+latent_dist = q(learned_params, D)(xtest)
+predictive_dist = likelihood(learned_params, latent_dist)
 
 samples = latent_dist.sample(seed=key, sample_shape=(20,))
 

examples/graph_kernels.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -143,8 +143,8 @@
 
 # %%
 initial_params = parameter_state.params
-initial_dist = likelihood(posterior(D, initial_params)(x), initial_params)
-predictive_dist = likelihood(posterior(D, learned_params)(x), learned_params)
+initial_dist = likelihood(initial_params, posterior(initial_params, D)(x))
+predictive_dist = likelihood(learned_params, posterior(learned_params, D)(x))
 
 initial_mean = initial_dist.mean()
 learned_mean = predictive_dist.mean()

examples/haiku.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -31,9 +31,13 @@
 from chex import dataclass
 from jax.config import config
 from scipy.signal import sawtooth
+from jaxtyping import Float, Array
+from typing import Dict
+
 
 import gpjax as gpx
 from gpjax.kernels import DenseKernelComputation, AbstractKernel
+from gpjax.types import PRNGKeyType
 
 # Enable Float64 for more stable matrix inversions.
 config.update("jax_enable_x64", True)
@@ -84,18 +88,18 @@ class _DeepKernelFunction:
 @dataclass
 class DeepKernelFunction(AbstractKernel, DenseKernelComputation, _DeepKernelFunction):
     def __call__(
-        self, x: jnp.DeviceArray, y: jnp.DeviceArray, params: dict
-    ) -> jnp.ndarray:
+        self, params: Dict, x: Float[Array, "1 D"], y: Float[Array, "1 D"], 
+    ) -> Float[Array, "1"]:
         xt = self.network.apply(params=params, x=x)
         yt = self.network.apply(params=params, x=y)
-        return self.base_kernel(xt, yt, params=params)
+        return self.base_kernel(params, xt, yt)
 
-    def initialise(self, dummy_x, key):
+    def initialise(self, dummy_x: Float[Array, "1 D"], key: PRNGKeyType) -> None:
         nn_params = self.network.init(rng=key, x=dummy_x)
         base_kernel_params = self.base_kernel._initialise_params(key)
         self._params = {**nn_params, **base_kernel_params}
 
-    def _initialise_params(self, key):
+    def _initialise_params(self, key: PRNGKeyType) -> Dict:
         return self._params
 
 
@@ -181,8 +185,8 @@ def forward(x):
 # With a set of learned parameters, the only remaining task is to predict the output of the model. We can do this by simply applying the model to a test data set.
 
 # %%
-latent_dist = posterior(D, learned_params)(xtest)
-predictive_dist = likelihood(latent_dist, learned_params)
+latent_dist = posterior(learned_params, D)(xtest)
+predictive_dist = likelihood(learned_params, latent_dist)
 
 predictive_mean = predictive_dist.mean()
 predictive_std = predictive_dist.stddev()

examples/kernels.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -30,6 +30,7 @@
 from jax.config import config
 from jaxtyping import Array, Float
 from optax import adam
+from typing import Dict
 
 import gpjax as gpx
 
@@ -100,9 +101,17 @@
 # We'll now simulate some data and evaluate the kernel on the previously selected input dimensions.
 
 # %%
+# Inputs
 x_matrix = jr.normal(key, shape=(50, 5))
+
+# Gram kernel computation
 gram_fn = slice_kernel.gram
-K = gram_fn(slice_kernel, x_matrix, slice_kernel._initialise_params(key))
+
+# Default parameter dictionary
+params = slice_kernel._initialise_params(key)
+
+# Compute the Gram matrix
+K = gram_fn(slice_kernel, params, x_matrix)
 print(K.shape)
 
 # %% [markdown]
@@ -119,9 +128,9 @@
 sum_k = k1 + k2
 
 fig, ax = plt.subplots(ncols=3, figsize=(20, 5))
-im0 = ax[0].matshow(k1.gram(k1, x, k1._initialise_params(key)).to_dense())
-im1 = ax[1].matshow(k2.gram(k2, x, k2._initialise_params(key)).to_dense())
-im2 = ax[2].matshow(sum_k.gram(sum_k, x, sum_k._initialise_params(key)).to_dense())
+im0 = ax[0].matshow(k1.gram(k1, k1._initialise_params(key), x).to_dense())
+im1 = ax[1].matshow(k2.gram(k2, k2._initialise_params(key), x).to_dense())
+im2 = ax[2].matshow(sum_k.gram(sum_k, sum_k._initialise_params(key), x).to_dense())
 
 fig.colorbar(im0, ax=ax[0])
 fig.colorbar(im1, ax=ax[1])
@@ -136,10 +145,10 @@
 prod_k = k1 * k2 * k3
 
 fig, ax = plt.subplots(ncols=4, figsize=(20, 5))
-im0 = ax[0].matshow(k1.gram(k1, x, k1._initialise_params(key)).to_dense())
-im1 = ax[1].matshow(k2.gram(k2, x, k2._initialise_params(key)).to_dense())
-im2 = ax[2].matshow(k3.gram(k3, x, k3._initialise_params(key)).to_dense())
-im3 = ax[3].matshow(prod_k.gram(prod_k, x, prod_k._initialise_params(key)).to_dense())
+im0 = ax[0].matshow(k1.gram(k1, k1._initialise_params(key), x).to_dense())
+im1 = ax[1].matshow(k2.gram(k2, k2._initialise_params(key), x).to_dense())
+im2 = ax[2].matshow(k3.gram(k3, k3._initialise_params(key), x).to_dense())
+im3 = ax[3].matshow(prod_k.gram(prod_k, prod_k._initialise_params(key), x).to_dense())
 
 fig.colorbar(im0, ax=ax[0])
 fig.colorbar(im1, ax=ax[1])
@@ -206,7 +215,7 @@ def __post_init__(self):
         self.c = self.period / 2.0  # in [0, \pi]
 
     def __call__(
-        self, x: Float[Array, "1 D"], y: Float[Array, "1 D"], params: dict
+        self, params: Dict, x: Float[Array, "1 D"], y: Float[Array, "1 D"] 
     ) -> Float[Array, "1"]:
         tau = params["tau"]
         t = angular_distance(x, y, self.c)
@@ -248,15 +257,15 @@ def _initialise_params(self, key: jr.PRNGKey) -> dict:
 #
 #
 # ### Custom Parameter Bijection
-
+#
 # The constraint on $\tau$ makes optimisation challenging with gradient descent.
 # It would be much easier if we could instead parameterise $\tau$ to be on the
 # real line. Fortunately, this can be taken care of with GPJax's `add parameter`
 # function, only requiring us to define the parameter's name and matching
 # bijection (either a Distrax of TensorFlow probability bijector). Under the
 # hood, calling this function updates a configuration object to register this
 # parameter and its corresponding transform.
-
+#
 # To define a bijector here we'll make use of the `Lambda` operator given in
 # Distrax. This lets us convert any regular Jax function into a bijection. Given
 # that we require $\tau$ to be strictly greater than $4.$, we'll apply a
@@ -321,7 +330,7 @@ def _initialise_params(self, key: jr.PRNGKey) -> dict:
 
 # %%
 posterior_rv = likelihood(
-    circlular_posterior(D, learned_params)(angles), learned_params
+    learned_params, circlular_posterior(learned_params, D)(angles)
 )
 mu = posterior_rv.mean()
 one_sigma = posterior_rv.stddev()

examples/natgrads.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -108,7 +108,7 @@
 
 # %%
 latent_dist = natural_q(learned_params)(xtest)
-predictive_dist = likelihood(latent_dist, learned_params)
+predictive_dist = likelihood(learned_params, latent_dist)
 
 meanf = predictive_dist.mean()
 sigma = predictive_dist.stddev()
@@ -212,5 +212,3 @@
 # %%
 # %reload_ext watermark
 # %watermark -n -u -v -iv -w -a 'Daniel Dodd'
-
-# %%

examples/regression.pct.py

@@ -8,7 +8,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -200,8 +200,8 @@
 # Equipped with the posterior and a set of optimised hyperparameter values, we are now in a position to query our GP's predictive distribution at novel test inputs. To do this, we use our defined `posterior` and `likelihood` at our test inputs to obtain the predictive distribution as a `Distrax` multivariate Gaussian upon which `mean` and `stddev` can be used to extract the predictive mean and standard deviatation.
 
 # %%
-latent_dist = posterior(D, learned_params)(xtest)
-predictive_dist = likelihood(latent_dist, learned_params)
+latent_dist = posterior(learned_params, D)(xtest)
+predictive_dist = likelihood(learned_params, latent_dist)
 
 predictive_mean = predictive_dist.mean()
 predictive_std = predictive_dist.stddev()

examples/tfp_integration.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -95,7 +95,7 @@
 # %% [markdown]
 # ### Specifying priors
 #
-# We can define Gamma priors on our hyperparameters through TensorFlow Probability's `Distributions` module.
+# We can define Gamma priors on our hyperparameters through TensorFlow Probability's `Distributions` module. We transform these to the unconstained space via `tfd.TransformedDistribution`.
 
 # %%
 import tensorflow_probability.substrates.jax as tfp
@@ -209,7 +209,7 @@ def run_chain(key, state):
 xtest = jnp.linspace(-5.2, 5.2, 500).reshape(-1, 1)
 learned_params = array_to_dict([jnp.mean(i) for i in constrained_sample_list])
 
-predictive_dist = likelihood(posterior(D, learned_params)(xtest), learned_params)
+predictive_dist = likelihood(learned_params, posterior(learned_params, D)(xtest))
 
 mu = predictive_dist.mean()
 sigma = predictive_dist.stddev()

examples/uncollapsed_vi.pct.py

@@ -9,7 +9,7 @@
 #       format_version: '1.3'
 #       jupytext_version: 1.11.2
 #   kernelspec:
-#     display_name: Python 3.9.7 ('gpjax')
+#     display_name: base
 #     language: python
 #     name: python3
 # ---
@@ -176,7 +176,7 @@
 
 # %%
 latent_dist = q(learned_params)(xtest)
-predictive_dist = likelihood(latent_dist, learned_params)
+predictive_dist = likelihood(learned_params, latent_dist)
 
 meanf = predictive_dist.mean()
 sigma = predictive_dist.stddev()