BayesianQuadrature

class probnum.quad.BayesianQuadrature(kernel, measure, policy, belief_update, stopping_criterion)

Bases: object

The Bayesian quadrature method.

Bayesian quadrature solves integrals of the form

\[F = \int_\Omega f(x) d \mu(x).\]

Parameters

• kernel (Kernel) – The kernel used for the GP model.

• measure (IntegrationMeasure) – The integration measure.

• policy (Optional[Policy]) – The policy choosing nodes at which to evaluate the integrand.

• belief_update (BQBeliefUpdate) – The inference method.

• stopping_criterion (BQStoppingCriterion) – The criterion that determines convergence.

Return type

None

See also

bayesquad

Computes the integral using an acquisition policy.

bayesquad_from_data

Computes the integral \(F\) using a given dataset of nodes and function evaluations.

Methods Summary

bq_iterator(bq_state, info, fun)	Generator that implements the iteration of the BQ method.
from_problem(input_dim[, kernel, measure, ...])	Creates an instance of this class from a problem description.
integrate(fun, nodes, fun_evals)	Integrates the function fun.

Methods Documentation

bq_iterator(bq_state, info, fun)

Generator that implements the iteration of the BQ method.

This function exposes the state of the BQ method one step at a time while running the loop.

Parameters

• bq_state (BQState) – State of the Bayesian quadrature methods. Contains the information about the problem and the BQ belief.

• info (Optional[BQIterInfo]) – The state of the iteration.

• fun (Optional[Callable]) – Function to be integrated. It needs to accept a shape=(n_eval, input_dim) np.ndarray and return a shape=(n_eval,) np.ndarray.

Yields

• new_integral_belief – Updated belief about the integral.

• new_bq_state – The updated state of the Bayesian quadrature belief.

• new_info – The updated state of the iteration.

Return type

Tuple[Normal, BQState, BQIterInfo]

classmethod from_problem(input_dim, kernel=None, measure=None, domain=None, policy='bmc', max_evals=None, var_tol=None, rel_tol=None, batch_size=1, rng=None)

Creates an instance of this class from a problem description.

Parameters

• input_dim (int) – The input dimension.

• 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 on the domain.

• domain (Optional[Union[Tuple[Union[float, Real, floating], Union[float, Real, floating]], Tuple[ndarray, ndarray]]]) – The integration bounds. Obsolete if measure is given.

• policy (Optional[str]) – The policy choosing nodes at which to evaluate the integrand. Choose None if you want to integrate from a fixed dataset.

• max_evals (Optional[Union[int, Integral, integer]]) – Maximum number of evaluations as stopping criterion.

• var_tol (Optional[Union[float, Real, floating]]) – Variance tolerance as stopping criterion.

• rel_tol (Optional[Union[float, Real, floating]]) – Relative tolerance as stopping criterion.

• batch_size (Union[int, Integral, integer]) – Batch size used in node acquisition.

• rng (Optional[Generator]) – The random number generator.

Returns

An instance of this class.

Return type

BayesianQuadrature

Raises

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

• ValueError – If Bayesian Monte Carlo (‘bmc’) is selected as policy and no random number generator (rng) is given.

• NotImplementedError – If an unknown policy is given.

integrate(fun, nodes, fun_evals)

Integrates the function fun.

fun may be analytically given, or numerically in terms of fun_evals at fixed nodes. This function calls the generator bq_iterator until the first stopping criterion is met. It immediately stops after processing the initial nodes if policy is not available.

Parameters

• fun (Optional[Callable]) – Function to be integrated. It needs to accept a shape=(n_eval, input_dim) np.ndarray and return a shape=(n_eval,) np.ndarray.

• nodes (Optional[ndarray]) – shape=(n_eval, input_dim) – Optional nodes at which function evaluations are available as fun_evals from start.

• fun_evals (Optional[ndarray]) – shape=(n_eval,) – Optional function evaluations at nodes available from the start.

Returns

• integral_belief – Posterior belief about the integral.

• bq_state – Final state of the Bayesian quadrature method.

Raises

• ValueError – If neither the integrand function (fun) nor integrand evaluations (fun_evals) are given.

• ValueError – If nodes are not given and no policy is present.

• ValueError – If dimension of nodes or fun_evals is incorrect, or if their shapes do not match.

Return type

Tuple[Normal, BQState, BQIterInfo]