.. _sphx_glr_auto_examples_tree_plot_tree_regression_multioutput.py:


===================================================================
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.




.. image:: /auto_examples/tree/images/sphx_glr_plot_tree_regression_multioutput_001.png
    :align: center





.. code-block:: python

    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()
    s = 50
    s = 25
    plt.scatter(y[:, 0], y[:, 1], c="navy", s=s,
                edgecolor="black", label="data")
    plt.scatter(y_1[:, 0], y_1[:, 1], c="cornflowerblue", s=s,
                edgecolor="black", label="max_depth=2")
    plt.scatter(y_2[:, 0], y_2[:, 1], c="red", s=s,
                edgecolor="black", label="max_depth=5")
    plt.scatter(y_3[:, 0], y_3[:, 1], c="orange", s=s,
                edgecolor="black", label="max_depth=8")
    plt.xlim([-6, 6])
    plt.ylim([-6, 6])
    plt.xlabel("target 1")
    plt.ylabel("target 2")
    plt.title("Multi-output Decision Tree Regression")
    plt.legend(loc="best")
    plt.show()

**Total running time of the script:** ( 0 minutes  0.175 seconds)



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  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_tree_regression_multioutput.py <plot_tree_regression_multioutput.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_tree_regression_multioutput.ipynb <plot_tree_regression_multioutput.ipynb>`

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