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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()
```

**Total running time of the script:** (0 minutes 0.450 seconds)

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