Gradient Boosting Regression

Introduction

In this lab, we will use Gradient Boosting to build a predictive model for diabetes regression task. We will train the model on the diabetes dataset and obtain the results from sklearn.ensemble.GradientBoostingRegressor with least squares loss and 500 regression trees of depth 4.

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Skills Graph

Load the Data

First, we will load the diabetes dataset.

diabetes = datasets.load_diabetes()
X, y = diabetes.data, diabetes.target

Data Preprocessing

Next, we will split our dataset to use 90% for training and leave the rest for testing. We will also set the regression model parameters.

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=13)

params = {
    "n_estimators": 500,
    "max_depth": 4,
    "min_samples_split": 5,
    "learning_rate": 0.01,
    "loss": "squared_error",
}

Fit Regression Model

Now we will initiate the gradient boosting regressors and fit it with our training data. Let's also look and the mean squared error on the test data.

reg = ensemble.GradientBoostingRegressor(**params)
reg.fit(X_train, y_train)

mse = mean_squared_error(y_test, reg.predict(X_test))
print("The mean squared error (MSE) on test set: {:.4f}".format(mse))

Plot Training Deviance

Finally, we will visualize the results. To do that we will first compute the test set deviance and then plot it against boosting iterations.

test_score = np.zeros((params["n_estimators"],), dtype=np.float64)
for i, y_pred in enumerate(reg.staged_predict(X_test)):
    test_score[i] = mean_squared_error(y_test, y_pred)

fig = plt.figure(figsize=(6, 6))
plt.subplot(1, 1, 1)
plt.title("Deviance")
plt.plot(
    np.arange(params["n_estimators"]) + 1,
    reg.train_score_,
    "b-",
    label="Training Set Deviance",
)
plt.plot(
    np.arange(params["n_estimators"]) + 1, test_score, "r-", label="Test Set Deviance"
)
plt.legend(loc="upper right")
plt.xlabel("Boosting Iterations")
plt.ylabel("Deviance")
fig.tight_layout()
plt.show()

Plot Feature Importance

For this example, we will use impurity-based feature importances to identify the most predictive features.

feature_importance = reg.feature_importances_
sorted_idx = np.argsort(feature_importance)
pos = np.arange(sorted_idx.shape[0]) + 0.5
fig = plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.barh(pos, feature_importance[sorted_idx], align="center")
plt.yticks(pos, np.array(diabetes.feature_names)[sorted_idx])
plt.title("Feature Importance (MDI)")

Plot Permutation Importance

We will use the permutation method to identify the most predictive features.

result = permutation_importance(
    reg, X_test, y_test, n_repeats=10, random_state=42, n_jobs=2
)
sorted_idx = result.importances_mean.argsort()
plt.subplot(1, 2, 2)
plt.boxplot(
    result.importances[sorted_idx].T,
    vert=False,
    labels=np.array(diabetes.feature_names)[sorted_idx],
)
plt.title("Permutation Importance (test set)")
fig.tight_layout()
plt.show()

Summary

In this lab, we used Gradient Boosting to build a predictive model for diabetes regression task. We loaded the data, preprocessed it, fit the regression model, and visualized the results by plotting the training deviance, feature importance, and permutation importance.