📝 Exercise M6.03#

The aim of this exercise is to:

  • verifying if a random forest or a gradient-boosting decision tree overfit if the number of estimators is not properly chosen;

  • use the early-stopping strategy to avoid adding unnecessary trees, to get the best generalization performances.

We will use the California housing dataset to conduct our experiments.

from sklearn.datasets import fetch_california_housing
from sklearn.model_selection import train_test_split

data, target = fetch_california_housing(return_X_y=True, as_frame=True)
target *= 100  # rescale the target in k$
data_train, data_test, target_train, target_test = train_test_split(
    data, target, random_state=0, test_size=0.5)

Note

If you want a deeper overview regarding this dataset, you can refer to the Appendix - Datasets description section at the end of this MOOC.

Create a gradient boosting decision tree with max_depth=5 and learning_rate=0.5.

# Write your code here.

Also create a random forest with fully grown trees by setting max_depth=None.

# Write your code here.

For both the gradient-boosting and random forest models, create a validation curve using the training set to assess the impact of the number of trees on the performance of each model. Evaluate the list of parameters param_range = [1, 2, 5, 10, 20, 50, 100] and use the mean absolute error.

# Write your code here.

Both gradient boosting and random forest models will always improve when increasing the number of trees in the ensemble. However, it will reach a plateau where adding new trees will just make fitting and scoring slower.

To avoid adding new unnecessary tree, unlike random-forest gradient-boosting offers an early-stopping option. Internally, the algorithm will use an out-of-sample set to compute the generalization performance of the model at each addition of a tree. Thus, if the generalization performance is not improving for several iterations, it will stop adding trees.

Now, create a gradient-boosting model with n_estimators=1_000. This number of trees will be too large. Change the parameter n_iter_no_change such that the gradient boosting fitting will stop after adding 5 trees that do not improve the overall generalization performance.

# Write your code here.

Estimate the generalization performance of this model again using the sklearn.metrics.mean_absolute_error metric but this time using the test set that we held out at the beginning of the notebook. Compare the resulting value with the values observed in the validation curve.

# Write your code here.