class_docstr: 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 : float or array-like, optional (default: 1e-10)
      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 : string, "gaussian", optional
      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)
  
  kernel_ kernel object
      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_ : array-like, shape = (n_samples,)
      Dual coefficients of training data points in kernel space
  
  log_marginal_likelihood_value_ : float
      The log-marginal-likelihood of ``self.kernel_.theta``
  
  noise_ : float
      Estimate of the gaussian noise. Useful only when noise is set to
      "gaussian".
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code: def __init__(
      self,
      kernel=None,
      alpha=1e-10,
      optimizer="fmin_l_bfgs_b",
      n_restarts_optimizer=0,
      normalize_y=False,
      copy_X_train=True,
      random_state=None,
      noise=None,
  ):
      self.noise = noise
      super(GaussianProcessRegressor, self).__init__(
          kernel=kernel,
          alpha=alpha,
          optimizer=optimizer,
          n_restarts_optimizer=n_restarts_optimizer,
          normalize_y=normalize_y,
          copy_X_train=copy_X_train,
          random_state=random_state,
      )
  
file_path: scikit-optimize/skopt/learning/gaussian_process/gpr.py
imports: import numpy
  import warnings
  from scipy.linalg import cho_solve
  from scipy.linalg import solve_triangular
  import sklearn
  from sklearn.gaussian_process import GaussianProcessRegressor
  from sklearn.utils import check_array
  from .kernels import ConstantKernel
  from .kernels import Sum
  from .kernels import RBF
  from .kernels import WhiteKernel
label_desc: Use image node_id 1 to create a new GaussianProcessRegressor object from inherited base classes: sk_GaussianProcessRegressor with example: obj = GaussianProcessRegressor(kernel, alpha, optimizer, n_restarts_optimizer, normalize_y, copy_X_train, random_state, noise)