content: """
  ===================================================================
  Multi-output Decision Tree Regression
  ===================================================================
  
  An example to illustrate multi-output regression with decision tree.
  
  The :ref:`decision trees <tree>`
  is used to predict simultaneously the noisy x and y observations of a circle
  given a single underlying feature. As a result, it learns local linear
  regressions approximating the circle.
  
  We can see that if the maximum depth of the tree (controlled by the
  `max_depth` parameter) is set too high, the decision trees learn too fine
  details of the training data and learn from the noise, i.e. they overfit.
  """
  print(__doc__)
  
  import numpy as np
  import matplotlib.pyplot as plt
  from sklearn.tree import DecisionTreeRegressor
  
  # Create a random dataset
  rng = np.random.RandomState(1)
  X = np.sort(200 * rng.rand(100, 1) - 100, axis=0)
  y = np.array([np.pi * np.sin(X).ravel(), np.pi * np.cos(X).ravel()]).T
  y[::5, :] += (0.5 - rng.rand(20, 2))
  
  # Fit regression model
  regr_1 = DecisionTreeRegressor(max_depth=2)
  regr_2 = DecisionTreeRegressor(max_depth=5)
  regr_3 = DecisionTreeRegressor(max_depth=8)
  regr_1.fit(X, y)
  regr_2.fit(X, y)
  regr_3.fit(X, y)
  
  # Predict
  X_test = np.arange(-100.0, 100.0, 0.01)[:, np.newaxis]
  y_1 = regr_1.predict(X_test)
  y_2 = regr_2.predict(X_test)
  y_3 = regr_3.predict(X_test)
  
  # Plot the results
  plt.figure()
  plt.scatter(y[:, 0], y[:, 1], c="k", label="data")
  plt.scatter(y_1[:, 0], y_1[:, 1], c="g", label="max_depth=2")
  plt.scatter(y_2[:, 0], y_2[:, 1], c="r", label="max_depth=5")
  plt.scatter(y_3[:, 0], y_3[:, 1], c="b", label="max_depth=8")
  plt.xlim([-6, 6])
  plt.ylim([-6, 6])
  plt.xlabel("data")
  plt.ylabel("target")
  plt.title("Multi-output Decision Tree Regression")
  plt.legend()
  plt.show()
  