# skopt.acquisition.gaussian_ei¶

skopt.acquisition.gaussian_ei(X, model, y_opt=0.0, xi=0.01, return_grad=False)[source][source]

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 E[u(f(x))] where u(f(x)) = 0, if f(x) > y_opt and u(f(x)) = y_opt - f(x), iff(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 X with maximum improvement.

Parameters
Xarray-like, shape=(n_samples, n_features)

Values where the acquisition function should be computed.

modelsklearn estimator that implements predict with return_std

The fit estimator that approximates the function through the method predict. It should have a return_std parameter 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 method is set to “EI”

Whether or not to return the grad. Implemented only for the case where X is a single sample.