Bases: object

Bayesian quadrature solves integrals of the form

$F = \int_\Omega f(x) d \mu(x).$
Parameters
• kernel (Kernel) – The kernel used for the Gaussian process 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.

• initial_design (Optional[InitialDesign]) – The initial design chooses a set of nodes once, before the acquisition loop with the policy runs.

Raises

ValueError – If initial_design is given but policy is not given.

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, rng) 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[, rng]) Integrates a given function.

Methods Documentation

bq_iterator(bq_state, info, fun, rng)[source]

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 (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.

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

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
classmethod from_problem(input_dim, kernel=None, measure=None, domain=None, policy='bmc', initial_design=None, options=None)[source]

Creates an instance of this class from a problem description.

Parameters
• input_dim (IntLike) – The input dimension.

• kernel (Optional[CovarianceFunction]) – 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[DomainLike]) – 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.

• initial_design (Optional[str]) – The initial design chooses a set of nodes once, before the acquisition loop with the policy runs.

• 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’.

max_evalsOptional[IntLike]

Maximum number of evaluations as stopping criterion.

var_tolOptional[FloatLike]

Variance tolerance as stopping criterion.

rel_tolOptional[FloatLike]

Relative tolerance as stopping criterion.

jitterOptional[FloatLike]

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

batch_sizeOptional[IntLike]

Batch size used in node acquisition. Defaults to 1.

n_initial_design_nodesOptional[IntLike]

The number of nodes created by the initial design. Defaults to input_dim * 5 if an initial design is given.

n_candidatesOptional[IntLike]

The number of candidate nodes used by the policies that maximize an acquisition function by drawing random candidates. Defaults to 1e2. Applicable to policies ‘us_rand’, ‘mi_rand’ and ‘ivr_rand’.

n_restartsOptional[IntLike]

The number of restarts that the acquisition optimizer performs in order to find the maximizer. Defaults to 10. Applicable to policies ‘us’, ‘mi’ and ‘ivr’.

Returns

An instance of this class.

Return type

Raises
• NotImplementedError – If an unknown policy or an unknown initial_design is given.

• ValueError – If neither domain nor measure is given.

bayesquad :

For details on options for policy and initial_design.

integrate(fun, nodes, fun_evals, rng=None)[source]

Integrates a given function.

The function may be given as a function handle fun and/or numerically in terms of fun_evals at fixed nodes nodes.

If a policy is defined this method calls the generator bq_iterator until the first stopping criterion is met. The initial design is evaluated in a batch prior to running bq_iterator.

If no policy is defined this method immediately stops after processing the given nodes.

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.

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

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 dimension of nodes or fun_evals is incorrect, or if their shapes do not match.

• ValueError – If rng is not given but policy or initial_design requires it.

• ValueError – If a policy is available but fun is not given.

• ValueError – If no policy is available and no nodes are given.

Warns

UserWarning – When no policy is given and fun is ignored.

Return type

Notes

The initial design is evaluated prior to running the bq_iterator and hence may not obey the stopping criterion. For example, if stopping is induced via a maximum number of evaluations (max_evals) smaller than the batch size of the initial design, the initial design will be evaluated nevertheless.