gaussian_ei(X, model, y_opt=0.0, xi=0.01, return_grad=False)¶
Use the expected improvement to calculate the acquisition values.
The conditional probability
P(y=f(x) | x)form a gaussian with a certain mean and standard deviation approximated by the model.
The EI condition is derived by computing
u(f(x)) = 0, if
f(x) > y_optand
u(f(x)) = y_opt - f(x), if``f(x) < y_opt``.
This solves one of the issues of the PI condition by giving a reward proportional to the amount of improvement got.
Note that the value returned by this function should be maximized to obtain the
Xwith maximum improvement.
- Xarray-like, shape=(n_samples, n_features)
Values where the acquisition function should be computed.
- modelsklearn estimator that implements predict with
The fit estimator that approximates the function through the method
predict. It should have a
return_stdparameter that returns the standard deviation.
- y_optfloat, default 0
Previous minimum value which we would like to improve upon.
- xifloat, default=0.01
Controls how much improvement one wants over the previous best values. Useful only when
methodis set to “EI”
- return_gradboolean, optional
Whether or not to return the grad. Implemented only for the case where
Xis a single sample.
- valuesarray-like, shape=(X.shape,)
Acquisition function values computed at X.