"""
===================================================================
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

# 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
from sklearn.tree import DecisionTreeRegressor

clf_1 = DecisionTreeRegressor(max_depth=2)
clf_2 = DecisionTreeRegressor(max_depth=5)
clf_3 = DecisionTreeRegressor(max_depth=8)
clf_1.fit(X, y)
clf_2.fit(X, y)
clf_3.fit(X, y)

# Predict
X_test = np.arange(-100.0, 100.0, 0.01)[:, np.newaxis]
y_1 = clf_1.predict(X_test)
y_2 = clf_2.predict(X_test)
y_3 = clf_3.predict(X_test)

# Plot the results
import pylab as pl

pl.figure()
pl.scatter(y[:, 0], y[:, 1], c="k", label="data")
pl.scatter(y_1[:, 0], y_1[:, 1], c="g", label="max_depth=2")
pl.scatter(y_2[:, 0], y_2[:, 1], c="r", label="max_depth=5")
pl.scatter(y_3[:, 0], y_3[:, 1], c="b", label="max_depth=8")
pl.xlim([-6, 6])
pl.ylim([-6, 6])
pl.xlabel("data")
pl.ylabel("target")
pl.title("Multi-output Decision Tree Regression")
pl.legend()
pl.show()