An example to illustrate multi-output regression with decision tree.
The decision trees 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() s = 50 plt.scatter(y[:, 0], y[:, 1], c="navy", s=s, label="data") plt.scatter(y_1[:, 0], y_1[:, 1], c="cornflowerblue", s=s, label="max_depth=2") plt.scatter(y_2[:, 0], y_2[:, 1], c="c", s=s, label="max_depth=5") plt.scatter(y_3[:, 0], y_3[:, 1], c="orange", s=s, 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() plt.show()
Total running time of the script: (0 minutes 0.221 seconds)
Download Python source code:
plot_tree_regression_multioutput.py
Download IPython notebook:
plot_tree_regression_multioutput.ipynb
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