MutualInformation

class probnum.quad.solvers.acquisition_functions.MutualInformation

Bases: AcquisitionFunction

The mutual information between a hypothetical integrand observation and the integral value.

The acquisition function is

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

where \(\rho^2(x)\) is the squared correlation between a hypothetical integrand observations at \(x\) and the integral value. 1

The mutual information is non-negative and unbounded for a ‘perfect’ observation and \(\rho^2(x) = 1.\)

References

1

Gessner et al. Active Multi-Information Source Bayesian Quadrature, UAI, 2019

Attributes Summary

has_gradients

Whether the acquisition function exposes gradients.

Methods Summary

__call__(x, bq_state)

Evaluates the acquisition function and optionally its gradients.

Attributes Documentation

has_gradients

Methods Documentation

__call__(x, bq_state)

Evaluates the acquisition function and optionally its gradients.

Parameters

• x (ndarray) – shape=(batch_size, input_dim) – The nodes where the acquisition function is being evaluated.

• bq_state (BQState) – State of the BQ belief.

Returns

• acquisition_values – shape=(batch_size, ) – The acquisition values at nodes x.

• acquisition_gradients – shape=(batch_size, input_dim) – The corresponding gradients (optional).

Return type

Tuple[ndarray, Optional[ndarray]]