Prior#

class gpjax.gps.Prior(kernel, mean_function, jitter=1e-06)[source]#

Bases: _SummaryMixin, Module, Generic[M, K]

A Gaussian process prior object.

A Gaussian process prior parameterised by a mean function \(m(\cdot)\) and a kernel function \(k(\cdot, \cdot)\) is given by \(p(f(\cdot)) = \mathcal{GP}(m(\cdot), k(\cdot, \cdot))\).

To invoke a Prior distribution, a kernel and mean function must be specified.

Example

>>> import gpjax as gpx
>>> kernel = gpx.kernels.RBF()
>>> meanf = gpx.mean_functions.Zero()
>>> prior = gpx.gps.Prior(mean_function=meanf, kernel = kernel)

See also

New to Gaussian Processes? derives the prior from first principles, and Regression puts one to work end to end.

Expand for references to gpjax.gps.Prior

Prior

GPJax / “Hello, GP!”

Migrations / 0.18.x → 1.0.0 / The conditioning API

fit

fit_natgrads

ConjugateModel

conjugate_loocv

StateSpacePrior

Parameters:

  • kernel (K)

  • mean_function (M)

  • jitter (float)

predict(test_inputs, *, covariance='dense')[source]#

Compute the prior predictive distribution at the test inputs.

Example

>>> import gpjax as gpx
>>> import jax.numpy as jnp
>>> kernel = gpx.kernels.RBF()
>>> mean_function = gpx.mean_functions.Zero()
>>> prior = gpx.gps.Prior(mean_function=mean_function, kernel=kernel)
>>> prior.predict(jnp.linspace(0, 1, 100)[:, None])
Parameters:

  • test_inputs (Float[Array, "N D"]) – The inputs at which to evaluate the prior distribution.

  • covariance (Literal['dense', 'diagonal']) – Whether to return the dense joint covariance at the test inputs or only the marginal (diagonal) variances.

Returns:

A multivariate normal random variable

representation of the Gaussian process.

Return type:

GaussianDistribution

Expand for references to gpjax.gps.Prior.predict

Prior

StateSpacePrior

sample_approx(num_samples, key, num_features=100)[source]#

Approximate samples from the Gaussian process prior.

Build an approximate sample from the Gaussian process prior via the finite feature approximation \(\hat{f}(x) = \sum_{i=1}^m\phi_i(x)\theta_i\) where \(\phi_i\) are \(m\) features sampled from the Fourier feature decomposition of the model’s kernel and \(\theta_i\) are samples from a unit Gaussian.

The same sample draw is evaluated for all queries, at constant cost per query.

Example

>>> import gpjax as gpx
>>> import jax.numpy as jnp
>>> import jax.random as jr
>>> key = jr.key(123)
>>>
>>> meanf = gpx.mean_functions.Zero()
>>> kernel = gpx.kernels.RBF(n_dims=1)
>>> prior = gpx.gps.Prior(mean_function=meanf, kernel = kernel)
>>>
>>> sample_fn = prior.sample_approx(10, key)
>>> sample_fn(jnp.linspace(0, 1, 100).reshape(-1, 1))
Parameters:

  • num_samples (int) – The desired number of samples.

  • key (KeyArray) – The random seed used for the sample(s).

  • num_features (int) – The number of features used when approximating the kernel.

Returns:

A function representing an approximate sample

from the Gaussian process prior.

Return type:

FunctionalSample

Expand for references to gpjax.gps.Prior.sample_approx

Prior