content: """
  =====================================
  Multi-class AdaBoosted Decision Trees
  =====================================
  
  This example reproduces Figure 1 of Zhu et al [1] and shows how boosting can
  improve prediction accuracy on a multi-class problem. The classification
  dataset is constructed by taking a ten-dimensional standard normal distribution
  and defining three classes separated by nested concentric ten-dimensional
  spheres such that roughly equal numbers of samples are in each class (quantiles
  of the :math:`\chi^2` distribution).
  
  The performance of the SAMME and SAMME.R [1] algorithms are compared. SAMME.R
  uses the probability estimates to update the additive model, while SAMME  uses
  the classifications only. As the example illustrates, the SAMME.R algorithm
  typically converges faster than SAMME, achieving a lower test error with fewer
  boosting iterations. The error of each algorithm on the test set after each
  boosting iteration is shown on the left, the classification error on the test
  set of each tree is shown in the middle, and the boost weight of each tree is
  shown on the right. All trees have a weight of one in the SAMME.R algorithm and
  therefore are not shown.
  
  .. [1] J. Zhu, H. Zou, S. Rosset, T. Hastie, "Multi-class AdaBoost", 2009.
  
  """
  print(__doc__)
  
  # Author: Noel Dawe <noel.dawe@gmail.com>
  #
  # License: BSD 3 clause
  
  from sklearn.externals.six.moves import zip
  
  import matplotlib.pyplot as plt
  
  from sklearn.datasets import make_gaussian_quantiles
  from sklearn.ensemble import AdaBoostClassifier
  from sklearn.metrics import accuracy_score
  from sklearn.tree import DecisionTreeClassifier
  
  
  X, y = make_gaussian_quantiles(n_samples=13000, n_features=10,
                                 n_classes=3, random_state=1)
  
  n_split = 3000
  
  X_train, X_test = X[:n_split], X[n_split:]
  y_train, y_test = y[:n_split], y[n_split:]
  
  bdt_real = AdaBoostClassifier(
      DecisionTreeClassifier(max_depth=2),
      n_estimators=600,
      learning_rate=1)
  
  bdt_discrete = AdaBoostClassifier(
      DecisionTreeClassifier(max_depth=2),
      n_estimators=600,
      learning_rate=1.5,
      algorithm="SAMME")
  
  bdt_real.fit(X_train, y_train)
  bdt_discrete.fit(X_train, y_train)
  
  real_test_errors = []
  discrete_test_errors = []
  
  for real_test_predict, discrete_train_predict in zip(
          bdt_real.staged_predict(X_test), bdt_discrete.staged_predict(X_test)):
      real_test_errors.append(
          1. - accuracy_score(real_test_predict, y_test))
      discrete_test_errors.append(
          1. - accuracy_score(discrete_train_predict, y_test))
  
  n_trees_discrete = len(bdt_discrete)
  n_trees_real = len(bdt_real)
  
  # Boosting might terminate early, but the following arrays are always
  # n_estimators long. We crop them to the actual number of trees here:
  discrete_estimator_errors = bdt_discrete.estimator_errors_[:n_trees_discrete]
  real_estimator_errors = bdt_real.estimator_errors_[:n_trees_real]
  discrete_estimator_weights = bdt_discrete.estimator_weights_[:n_trees_discrete]
  
  plt.figure(figsize=(15, 5))
  
  plt.subplot(131)
  plt.plot(range(1, n_trees_discrete + 1),
           discrete_test_errors, c='black', label='SAMME')
  plt.plot(range(1, n_trees_real + 1),
           real_test_errors, c='black',
           linestyle='dashed', label='SAMME.R')
  plt.legend()
  plt.ylim(0.18, 0.62)
  plt.ylabel('Test Error')
  plt.xlabel('Number of Trees')
  
  plt.subplot(132)
  plt.plot(range(1, n_trees_discrete + 1), discrete_estimator_errors,
           "b", label='SAMME', alpha=.5)
  plt.plot(range(1, n_trees_real + 1), real_estimator_errors,
           "r", label='SAMME.R', alpha=.5)
  plt.legend()
  plt.ylabel('Error')
  plt.xlabel('Number of Trees')
  plt.ylim((.2,
           max(real_estimator_errors.max(),
               discrete_estimator_errors.max()) * 1.2))
  plt.xlim((-20, len(bdt_discrete) + 20))
  
  plt.subplot(133)
  plt.plot(range(1, n_trees_discrete + 1), discrete_estimator_weights,
           "b", label='SAMME')
  plt.legend()
  plt.ylabel('Weight')
  plt.xlabel('Number of Trees')
  plt.ylim((0, discrete_estimator_weights.max() * 1.2))
  plt.xlim((-20, n_trees_discrete + 20))
  
  # prevent overlapping y-axis labels
  plt.subplots_adjust(wspace=0.25)
  plt.show()
  