bayesquad_from_data

probnum.quad.bayesquad_from_data(nodes, fun_evals, kernel=None, measure=None, domain=None, options=None)

Infer the value of an integral from a given set of nodes and function evaluations.

Parameters

  • nodes (np.ndarray) – shape=(n_eval, input_dim) – Locations at which the function evaluations are available as fun_evals.

  • fun_evals (np.ndarray) – shape=(n_eval,) – Function evaluations at nodes.

  • kernel (Optional[Kernel]) – The kernel used for the GP model. Defaults to the ExpQuad kernel.

  • measure (Optional[IntegrationMeasure]) – The integration measure. Defaults to the Lebesgue measure.

  • domain (Optional[DomainLike]) – The integration domain. Contains lower and upper bound as scalar or np.ndarray. Obsolete if measure is given.

  • options (Optional[dict]) –

    A dictionary with the following optional solver settings

    scale_estimationOptional[str]

    Estimation method to use to compute the scale parameter. Defaults to ‘mle’. Options are

    Maximum likelihood estimation

    mle
    jitterOptional[FloatLike]

    Non-negative jitter to numerically stabilise kernel matrix inversion. Defaults to 1e-8.

Returns

  • integral – The integral belief subject to the provided measure or domain.

  • info – Information on the performance of the method.

Raises

ValueError – If neither a domain nor a measure are given.

Warns

UserWarning – When domain is given but not used.

Return type

Tuple[Normal, BQIterInfo]

See also

bayesquad

Computes the integral using an acquisition policy.

Examples

>>> import numpy as np
>>> domain = (0, 1)
>>> nodes = np.linspace(0, 1, 15)[:, None]
>>> fun_evals = nodes.reshape(-1, )
>>> F, info = bayesquad_from_data(nodes=nodes, fun_evals=fun_evals, domain=domain)
>>> print(F.mean)
0.5