deephyper.skopt.learning.gaussian_process.GaussianProcessRegressor

deephyper.skopt.learning.gaussian_process.GaussianProcessRegressor#

class deephyper.skopt.learning.gaussian_process.GaussianProcessRegressor(*args: Any, **kwargs: Any)[source]#

Bases: GaussianProcessRegressor

GaussianProcessRegressor that allows noise tunability.

The implementation is based on Algorithm 2.1 of Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams.

In addition to standard scikit-learn estimator API, GaussianProcessRegressor:

allows prediction without prior fitting (based on the GP prior);

provides an additional method sample_y(X), which evaluates samples drawn from the GPR (prior or posterior) at given inputs;

exposes a method log_marginal_likelihood(theta), which can be used externally for other ways of selecting hyperparameters, e.g., via Markov chain Monte Carlo.

Parameters:

kernel (kernel object) – The kernel specifying the covariance function of the GP. If None is passed, the kernel “1.0 * RBF(1.0)” is used as default. Note that the kernel’s hyperparameters are optimized during fitting.
alpha (array-like, shape = (n_samples,)) – Value added to the diagonal of the kernel matrix during fitting. Larger values correspond to increased noise level in the observations and reduce potential numerical issue during fitting. If an array is passed, it must have the same number of entries as the data used for fitting and is used as datapoint-dependent noise level. Note that this is equivalent to adding a WhiteKernel with c=alpha. Allowing to specify the noise level directly as a parameter is mainly for convenience and for consistency with Ridge.

optimizer (string or callable, optional (default: "fmin_l_bfgs_b")) –

Can either be one of the internally supported optimizers for optimizing the kernel’s parameters, specified by a string, or an externally defined optimizer passed as a callable. If a callable is passed, it must have the signature:

def optimizer(obj_func, initial_theta, bounds):
    # * 'obj_func' is the objective function to be maximized, which
    #   takes the hyperparameters theta as parameter and an
    #   optional flag eval_gradient, which determines if the
    #   gradient is returned additionally to the function value
    # * 'initial_theta': the initial value for theta, which can be
    #   used by local optimizers
    # * 'bounds': the bounds on the values of theta
    ....
    # Returned are the best found hyperparameters theta and
    # the corresponding value of the target function.
    return theta_opt, func_min

Per default, the ‘fmin_l_bfgs_b’ algorithm from scipy.optimize is used. If None is passed, the kernel’s parameters are kept fixed. Available internal optimizers are:

'fmin_l_bfgs_b'

n_restarts_optimizer (int, optional (default: 0)) – The number of restarts of the optimizer for finding the kernel’s parameters which maximize the log-marginal likelihood. The first run of the optimizer is performed from the kernel’s initial parameters, the remaining ones (if any) from thetas sampled log-uniform randomly from the space of allowed theta-values. If greater than 0, all bounds must be finite. Note that n_restarts_optimizer == 0 implies that one run is performed.
normalize_y (boolean, optional (default: False)) – Whether the target values y are normalized, i.e., the mean of the observed target values become zero. This parameter should be set to True if the target values’ mean is expected to differ considerable from zero. When enabled, the normalization effectively modifies the GP’s prior based on the data, which contradicts the likelihood principle; normalization is thus disabled per default.
copy_X_train (bool, optional (default: True)) – If True, a persistent copy of the training data is stored in the object. Otherwise, just a reference to the training data is stored, which might cause predictions to change if the data is modified externally.
random_state (integer or numpy.RandomState, optional) – The generator used to initialize the centers. If an integer is given, it fixes the seed. Defaults to the global numpy random number generator.
noise (float) – If set to “gaussian”, then it is assumed that y is a noisy estimate of f(x) where the noise is gaussian.
Attributes
----------
X_train (array-like, shape = (n_samples, n_features)) – Feature values in training data (also required for prediction)
y_train (array-like, shape = (n_samples, [n_output_dims])) – Target values in training data (also required for prediction)
object (kernel kernel) – The kernel used for prediction. The structure of the kernel is the same as the one passed as parameter but with optimized hyperparameters
L (array-like, shape = (n_samples, n_samples)) – Lower-triangular Cholesky decomposition of the kernel in X_train_
alpha – Dual coefficients of training data points in kernel space
log_marginal_likelihood_value (float) – The log-marginal-likelihood of self.kernel_.theta
noise – Estimate of the gaussian noise. Useful only when noise is set to “gaussian”.

Methods

`fit`	Fit Gaussian process regression model.
`predict`	Predict output for X.

__call__(*args: Any, **kwargs: Any) → Any#: Call self as a function.

fit(X, y)[source]#

Fit Gaussian process regression model.

Args: X : array-like, shape = (n_samples, n_features)

Training data

yarray-like, shape = (n_samples, [n_output_dims]): Target values

Returns: self

Returns an instance of self.

predict(X, return_std=False, return_cov=False, return_mean_grad=False, return_std_grad=False)[source]#

Predict output for X.

In addition to the mean of the predictive distribution, also its standard deviation (return_std=True) or covariance (return_cov=True), the gradient of the mean and the standard-deviation with respect to X can be optionally provided.

Args: X : array-like, shape = (n_samples, n_features)

Query points where the GP is evaluated.

return_stdbool, default: False: If True, the standard-deviation of the predictive distribution at the query points is returned along with the mean.
return_covbool, default: False: If True, the covariance of the joint predictive distribution at the query points is returned along with the mean.
return_mean_gradbool, default: False: Whether or not to return the gradient of the mean. Only valid when X is a single point.
return_std_gradbool, default: False: Whether or not to return the gradient of the std. Only valid when X is a single point.

Returns: y_mean : array, shape = (n_samples, [n_output_dims])

Mean of predictive distribution a query points

y_stdarray, shape = (n_samples,), optional: Standard deviation of predictive distribution at query points. Only returned when return_std is True.
y_covarray, shape = (n_samples, n_samples), optional: Covariance of joint predictive distribution a query points. Only returned when return_cov is True.
y_mean_gradshape = (n_samples, n_features): The gradient of the predicted mean
y_std_gradshape = (n_samples, n_features): The gradient of the predicted std.

deephyper.skopt.learning.gaussian_process.GaussianProcessRegressor

Contents

deephyper.skopt.learning.gaussian_process.GaussianProcessRegressor#