content: #!/usr/bin/python
  # -*- coding: utf-8 -*-
  
  """
  ========================================================================
  Gaussian Processes regression: goodness-of-fit on the 'diabetes' dataset
  ========================================================================
  
  In this example, we fit a Gaussian Process model onto the diabetes
  dataset.
  
  We determine the correlation parameters with maximum likelihood
  estimation (MLE). We use an anisotropic squared exponential
  correlation model with a constant regression model. We also use a
  nugget of 1e-2 to account for the (strong) noise in the targets.
  
  We compute a cross-validation estimate of the coefficient of
  determination (R2) without reperforming MLE, using the set of correlation
  parameters found on the whole dataset.
  """
  print(__doc__)
  
  # Author: Vincent Dubourg <vincent.dubourg@gmail.com>
  # Licence: BSD 3 clause
  
  from sklearn import datasets
  from sklearn.gaussian_process import GaussianProcess
  from sklearn.cross_validation import cross_val_score, KFold
  
  # Load the dataset from scikit's data sets
  diabetes = datasets.load_diabetes()
  X, y = diabetes.data, diabetes.target
  
  # Instanciate a GP model
  gp = GaussianProcess(regr='constant', corr='absolute_exponential',
                       theta0=[1e-4] * 10, thetaL=[1e-12] * 10,
                       thetaU=[1e-2] * 10, nugget=1e-2, optimizer='Welch')
  
  # Fit the GP model to the data performing maximum likelihood estimation
  gp.fit(X, y)
  
  # Deactivate maximum likelihood estimation for the cross-validation loop
  gp.theta0 = gp.theta_  # Given correlation parameter = MLE
  gp.thetaL, gp.thetaU = None, None  # None bounds deactivate MLE
  
  # Perform a cross-validation estimate of the coefficient of determination using
  # the cross_validation module using all CPUs available on the machine
  K = 20  # folds
  R2 = cross_val_score(gp, X, y=y, cv=KFold(y.size, K), n_jobs=1).mean()
  print("The %d-Folds estimate of the coefficient of determination is R2 = %s"
        % (K, R2))
  