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# HuberRegressor vs Ridge on dataset with strong outliers

Fit Ridge and HuberRegressor on a dataset with outliers.

The example shows that the predictions in ridge are strongly influenced by the outliers present in the dataset. The Huber regressor is less influenced by the outliers since the model uses the linear loss for these. As the parameter epsilon is increased for the Huber regressor, the decision function approaches that of the ridge.

    # Authors: Manoj Kumar mks542@nyu.edu
    # License: BSD 3 clause

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import make_regression
    from sklearn.linear_model import HuberRegressor, Ridge

    # Generate toy data.
    rng = np.random.RandomState(0)
    X, y = make_regression(
        n_samples=20, n_features=1, random_state=0, noise=4.0, bias=100.0
    )

    # Add four strong outliers to the dataset.
    X_outliers = rng.normal(0, 0.5, size=(4, 1))
    y_outliers = rng.normal(0, 2.0, size=4)
    X_outliers[:2, :] += X.max() + X.mean() / 4.0
    X_outliers[2:, :] += X.min() - X.mean() / 4.0
    y_outliers[:2] += y.min() - y.mean() / 4.0
    y_outliers[2:] += y.max() + y.mean() / 4.0
    X = np.vstack((X, X_outliers))
    y = np.concatenate((y, y_outliers))
    plt.plot(X, y, "b.")

    # Fit the huber regressor over a series of epsilon values.
    colors = ["r-", "b-", "y-", "m-"]

    x = np.linspace(X.min(), X.max(), 7)
    epsilon_values = [1, 1.5, 1.75, 1.9]
    for k, epsilon in enumerate(epsilon_values):
        huber = HuberRegressor(alpha=0.0, epsilon=epsilon)
        huber.fit(X, y)
        coef_ = huber.coef_ * x + huber.intercept_
        plt.plot(x, coef_, colors[k], label="huber loss, %s" % epsilon)

    # Fit a ridge regressor to compare it to huber regressor.
    ridge = Ridge(alpha=0.0, random_state=0)
    ridge.fit(X, y)
    coef_ridge = ridge.coef_
    coef_ = ridge.coef_ * x + ridge.intercept_
    plt.plot(x, coef_, "g-", label="ridge regression")

    plt.title("Comparison of HuberRegressor vs Ridge")
    plt.xlabel("X")
    plt.ylabel("y")
    plt.legend(loc=0)
    plt.show()

Total running time of the script: (0 minutes 0.069 seconds)

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