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Decision Tree Regression with AdaBoost#

A decision tree is boosted using the AdaBoost.R2 [1] algorithm on a 1D sinusoidal dataset with a small amount of Gaussian noise. 299 boosts (300 decision trees) is compared with a single decision tree regressor. As the number of boosts is increased the regressor can fit more detail.

Preparing the data#

First, we prepare dummy data with a sinusoidal relationship and some gaussian noise.

# Author: Noel Dawe <noel.dawe@gmail.com>
#
# License: BSD 3 clause

import numpy as np

rng = np.random.RandomState(1)
X = np.linspace(0, 6, 100)[:, np.newaxis]
y = np.sin(X).ravel() + np.sin(6 * X).ravel() + rng.normal(0, 0.1, X.shape[0])

Training and prediction with DecisionTree and AdaBoost Regressors#

Now, we define the classifiers and fit them to the data. Then we predict on that same data to see how well they could fit it. The first regressor is a DecisionTreeRegressor with max_depth=4. The second regressor is an AdaBoostRegressor with a DecisionTreeRegressor of max_depth=4 as base learner and will be built with n_estimators=300 of those base learners.

from sklearn.ensemble import AdaBoostRegressor
from sklearn.tree import DecisionTreeRegressor

regr_1 = DecisionTreeRegressor(max_depth=4)

regr_2 = AdaBoostRegressor(
    DecisionTreeRegressor(max_depth=4), n_estimators=300, random_state=rng
)

regr_1.fit(X, y)
regr_2.fit(X, y)

y_1 = regr_1.predict(X)
y_2 = regr_2.predict(X)

Plotting the results#

Finally, we plot how well our two regressors, single decision tree regressor and AdaBoost regressor, could fit the data.

import matplotlib.pyplot as plt
import seaborn as sns

colors = sns.color_palette("colorblind")

plt.figure()
plt.scatter(X, y, color=colors[0], label="training samples")
plt.plot(X, y_1, color=colors[1], label="n_estimators=1", linewidth=2)
plt.plot(X, y_2, color=colors[2], label="n_estimators=300", linewidth=2)
plt.xlabel("data")
plt.ylabel("target")
plt.title("Boosted Decision Tree Regression")
plt.legend()
plt.show()