emukit.quadrature.acquisitions package

Module contents

Acquisition functions for the quadrature package.

class emukit.quadrature.acquisitions.MutualInformation(model)

Bases: Acquisition

The mutual information between the integral value and integrand evaluations under a Gaussian process model.

The mutual information is a monotonic transformation of the squared correlation, hence it yields the same acquisition policy under a standard Gaussian process model.

\[a(x) = -0.5 \log(1-\rho^2(x))\]

where \(\rho^2\) is the squared correlation.

Parameters

model (VanillaBayesianQuadrature) – A vanilla Bayesian quadrature model.

property has_gradients: bool

Whether acquisition value has analytical gradient calculation available.

Return type

bool

evaluate(x)

Evaluates the acquisition function at x.

Parameters

x (ndarray) – The locations where to evaluate, shape (n_points, input_dim) .

Return type

ndarray

Returns

The acquisition values at x, shape (n_points, 1).

evaluate_with_gradients(x)

Evaluate the acquisition function and its gradient.

Parameters

x (ndarray) – The locations where to evaluate, shape (n_points, input_dim) .

Return type

Tuple[ndarray, ndarray]

Returns

The acquisition values and corresponding gradients at x, shapes (n_points, 1) and (n_points, input_dim)

emukit.quadrature.acquisitions.IntegralVarianceReduction

alias of SquaredCorrelation

class emukit.quadrature.acquisitions.SquaredCorrelation(model)

Bases: Acquisition

The squared correlation between the integral value and integrand evaluations under a Gaussian process model.

\[a(x) = \frac{(\int k_N(s, x)p(s)\mathrm{d}s)^2}{\mathfrak{v}_N v_N(x)}\in [0, 1]\]

where \(\mathfrak{v}_N\) is the current integral variance given \(N\) observations, \(v_N(x)\) is the predictive integral variance if point \(x\) was added newly, and \(k_N(s, x)\) is the posterior kernel function.

Note

The squared correlation is identical to the integral-variance-reduction acquisition up to a global normalizing constant under a standard Gaussian process model.

Parameters

model (VanillaBayesianQuadrature) – A vanilla Bayesian quadrature model.

property has_gradients: bool

Whether acquisition value has analytical gradient calculation available.

Return type

bool

evaluate(x)

Evaluates the acquisition function at x.

Parameters

x (ndarray) – The locations where to evaluate, shape (n_points, input_dim) .

Return type

ndarray

Returns

The acquisition values at x, shape (n_points, 1).

evaluate_with_gradients(x)

Evaluate the acquisition function and its gradient.

Parameters

x (ndarray) – The locations where to evaluate, shape (n_points, input_dim).

Return type

Tuple[ndarray, ndarray]

Returns

The acquisition values and corresponding gradients at x, shapes (n_points, 1) and (n_points, input_dim)

class emukit.quadrature.acquisitions.UncertaintySampling(model, measure_power=2)

Bases: Acquisition

Uncertainty sampling.

\[a(x) = \operatorname{var}(f(x)) p(x)^q\]

where \(p(x)\) is the density of the integration measure, \(\operatorname{var}(f(x))\) is the predictive variance of the model at \(x\) and \(q\) is the measure_power parameter.

Parameters
  • model (IDifferentiable) – A warped Bayesian quadrature model that has gradients.

  • measure_power (float) – The power \(q\) of the measure. Default is 2.

property has_gradients: bool

Whether acquisition value has analytical gradient calculation available.

Return type

bool

evaluate(x)

Evaluates the acquisition function at x.

Parameters

x (ndarray) – The locations where to evaluate, shape (n_points, input_dim) .

Return type

ndarray

Returns

The acquisition values at x, shape (n_points, 1).

evaluate_with_gradients(x)

Evaluate the acquisition function and its gradient.

Parameters

x (ndarray) – The locations where to evaluate, shape (n_points, input_dim).

Return type

Tuple[ndarray, ndarray]

Returns

The acquisition values and corresponding gradients at x, shapes (n_points, 1) and (n_points, input_dim)