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.

[1]

H. Drucker, “Improving Regressors using Boosting Techniques”, 1997.

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()