# 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

Methods Summary

 __call__(x, bq_state) Evaluates the acquisition function and optionally its gradients.

Attributes Documentation

Methods Documentation

__call__(x, bq_state)[source]

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_valuesshape=(batch_size, ) – The acquisition values at nodes x.