@pytest.mark.parametrize("loss", ("log_loss", "exponential"))
def test_classification_synthetic(loss, global_random_seed):
    # Test GradientBoostingClassifier on synthetic dataset used by
    # Hastie et al. in ESLII - Figure 10.9
    X, y = datasets.make_hastie_10_2(n_samples=12000, random_state=global_random_seed)

    X_train, X_test = X[:2000], X[2000:]
    y_train, y_test = y[:2000], y[2000:]

    # Increasing the number of trees should decrease the test error
    common_params = {
        "max_depth": 1,
        "learning_rate": 1.0,
        "loss": loss,
        "random_state": global_random_seed,
    }
    gbrt_100_stumps = GradientBoostingClassifier(n_estimators=100, **common_params)
    gbrt_100_stumps.fit(X_train, y_train)

    gbrt_200_stumps = GradientBoostingClassifier(n_estimators=200, **common_params)
    gbrt_200_stumps.fit(X_train, y_train)

    assert gbrt_100_stumps.score(X_test, y_test) < gbrt_200_stumps.score(X_test, y_test)

    # Decision stumps are better suited for this dataset with a large number of
    # estimators.
    common_params = {
        "n_estimators": 200,
        "learning_rate": 1.0,
        "loss": loss,
        "random_state": global_random_seed,
    }
    gbrt_stumps = GradientBoostingClassifier(max_depth=1, **common_params)
    gbrt_stumps.fit(X_train, y_train)

    gbrt_10_nodes = GradientBoostingClassifier(max_leaf_nodes=10, **common_params)
    gbrt_10_nodes.fit(X_train, y_train)

    assert gbrt_stumps.score(X_test, y_test) > gbrt_10_nodes.score(X_test, y_test)

def test_regression_synthetic(global_random_seed):
    # Test on synthetic regression datasets used in Leo Breiman,
    # `Bagging Predictors?. Machine Learning 24(2): 123-140 (1996).
    random_state = check_random_state(global_random_seed)
    regression_params = {
        "n_estimators": 100,
        "max_depth": 4,
        "min_samples_split": 2,
        "learning_rate": 0.1,
        "loss": "squared_error",
    }

    # Friedman1
    X, y = datasets.make_friedman1(n_samples=1200, random_state=random_state, noise=1.0)
    X_train, y_train = X[:200], y[:200]
    X_test, y_test = X[200:], y[200:]

    clf = GradientBoostingRegressor()
    clf.fit(X_train, y_train)
    mse = mean_squared_error(y_test, clf.predict(X_test))
    assert mse < 5.5

    # Friedman2
    X, y = datasets.make_friedman2(n_samples=1200, random_state=random_state)
    X_train, y_train = X[:200], y[:200]
    X_test, y_test = X[200:], y[200:]

    clf = GradientBoostingRegressor(**regression_params)
    clf.fit(X_train, y_train)
    mse = mean_squared_error(y_test, clf.predict(X_test))
    assert mse < 2500.0

    # Friedman3
    X, y = datasets.make_friedman3(n_samples=1200, random_state=random_state)
    X_train, y_train = X[:200], y[:200]
    X_test, y_test = X[200:], y[200:]

    clf = GradientBoostingRegressor(**regression_params)
    clf.fit(X_train, y_train)
    mse = mean_squared_error(y_test, clf.predict(X_test))
    assert mse < 0.025