Models¶

class mini_gpr.models.Model( kernel, noise=1e-08, solver=<function vanilla>, )[source]¶

Parameters:

kernel (Kernel)
noise (float)
solver (LinearSolver)

abstractmethod fit(X, y)[source]¶

Fit the model to the data.

Parameters:

X (Float[ndarray, 'N D']) – the data points.
y (Float[ndarray, 'N']) – the target values.

abstractmethod predict(T)[source]¶

Get the predictive mean of the function at the given locations.

Parameters:: T (Float[ndarray, 'T D']) – the data points/locations at which to make predictions
Return type:: Float[ndarray, ‘T’]

abstractmethod latent_uncertainty(T)[source]¶

Get the latent uncertainty of the function at the given locations.

Parameters:: T (Float[ndarray, 'T D']) – the data points/locations at which to get the latent uncertainty
Return type:: Float[ndarray, ‘T’]

predictive_uncertainty(T)[source]¶

Get the predictive uncertainty of the function at the given locations.

Parameters:: T (Float[ndarray, 'T D']) – the data points/locations at which to get the predictive uncertainty
Return type:: Float[ndarray, ‘T’]

abstract property log_likelihood: float¶: Get the log marginal likelihood of the model conditioned on the training data.

sample_prior( locations, n_samples=1, *, rng=None, jitter=1e-08, )[source]¶

Generate samples from the model’s prior distribution.

Parameters:

locations (Float[ndarray, 'N D']) – the data points/locations at which to generate samples
n_samples (int) – the number of samples to generate
rng (RandomState | int | None) – the random number generator to use
jitter (float) – a small value to add to the diagonal of the kernel matrix to ensure numerical stability

Return type:

Float[ndarray, ‘n N’]

abstractmethod sample_posterior( locations, n_samples=1, *, rng=None, jitter=1e-06, )[source]¶

Generate samples from the model’s posterior distribution.

Parameters:

locations (Float[ndarray, 'N D']) – the data points/locations at which to generate samples
n_samples (int) – the number of samples to generate
rng (RandomState | int | None) – the random number generator to use
jitter (float) – a small value to add to the diagonal of the kernel matrix to ensure numerical stability

Return type:

Float[ndarray, ‘n N’]

class mini_gpr.models.GPR( kernel, noise=1e-08, solver=<function vanilla>, )[source]¶

Bases: Model

Full-rank Gaussian Process Regression model.

Parameters:

kernel (Kernel) – defines the covariance between data points.
noise (float) – the aleatoric noise assumed to be present in the data.
solver (LinearSolver) – solver of linear systems of the form A @ x = y.

Example

>>> from mini_gpr.kernels import RBF
>>> from mini_gpr.models import GPR
>>> model = GPR(kernel=RBF(), noise=1e-3)
>>> model.fit(X, y)
>>> predictions = model.predict(T) # (T,)
>>> uncertainties = model.predictive_uncertainty(T) # (T,)

class mini_gpr.models.SoR( kernel, sparse_points, noise=1e-08, solver=<function vanilla>, )[source]¶

Bases: Model

Subset of Regressors low-rank Gaussian Process Regression approximation.

Parameters:

kernel (Kernel) – defines the covariance between data points.
sparse_points (Float[ndarray, 'M D']) – the inducing points.
noise (float) – the aleatoric noise assumed to be present in the data.
solver (LinearSolver) – solver of linear systems of the form A @ x = y.

Example

>>> from mini_gpr.kernels import RBF
>>> from mini_gpr.models import SoR
>>> model = SoR(
...    kernel=RBF(), sparse_points=np.random.rand(10, 2), noise=1e-3
... )
>>> model.fit(X, y)
>>> predictions = model.predict(T) # (T,)
>>> uncertainties = model.latent_uncertainty(T) # (T,)

Solvers¶

class mini_gpr.solvers.LinearSolver(*args, **kwargs)[source]¶: Solve a linear system of the form A @ x = y.

class mini_gpr.solvers.vanilla(A, y)[source]¶: Use the standard np.linalg.solve method to solve the linear system.

class mini_gpr.solvers.least_squares(A, y)[source]¶: Use np.linalg.lstsq method to solve the linear system: slower than vanilla but more stable.