"""Gaussian processes."""
import numpy as np
from probnum import randvars
from . import _random_process, kernels
from .. import _function
from ..typing import ArrayLike
class GaussianProcess(_random_process.RandomProcess[ArrayLike, np.ndarray]):
"""Gaussian processes.
A Gaussian process is a continuous stochastic process which if evaluated at a
finite set of inputs returns a random variable with a normal distribution. Gaussian
processes are fully characterized by their mean and covariance function.
Parameters
----------
mean :
Mean function.
cov :
Covariance function or kernel.
See Also
--------
RandomProcess : Random processes.
MarkovProcess : Random processes with the Markov property.
Examples
--------
Define a Gaussian process with a zero mean function and RBF kernel.
>>> import numpy as np
>>> from probnum.randprocs.mean_fns import Zero
>>> from probnum.randprocs.kernels import ExpQuad
>>> from probnum.randprocs import GaussianProcess
>>> mu = Zero(input_shape=()) # zero-mean function
>>> k = ExpQuad(input_shape=()) # RBF kernel
>>> gp = GaussianProcess(mu, k)
Sample from the Gaussian process.
>>> x = np.linspace(-1, 1, 5)
>>> rng = np.random.default_rng(seed=42)
>>> gp.sample(rng, x)
array([-0.7539949 , -0.6658092 , -0.52972512, 0.0674298 , 0.72066223])
>>> gp.cov.matrix(x)
array([[1. , 0.8824969 , 0.60653066, 0.32465247, 0.13533528],
[0.8824969 , 1. , 0.8824969 , 0.60653066, 0.32465247],
[0.60653066, 0.8824969 , 1. , 0.8824969 , 0.60653066],
[0.32465247, 0.60653066, 0.8824969 , 1. , 0.8824969 ],
[0.13533528, 0.32465247, 0.60653066, 0.8824969 , 1. ]])
"""
def __init__(
self,
mean: _function.Function,
cov: kernels.Kernel,
):
if not isinstance(mean, _function.Function):
raise TypeError("The mean function must have type `probnum.Function`.")
super().__init__(
input_shape=mean.input_shape,
output_shape=mean.output_shape,
dtype=np.dtype(np.float_),
mean=mean,
cov=cov,
)
[docs] def __call__(self, args: ArrayLike) -> randvars.Normal:
return randvars.Normal(
mean=np.array(self.mean(args), copy=False), # pylint: disable=not-callable
cov=self.cov.matrix(args),
)