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scikit-learn 1.3.2
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# Robust linear model estimation using RANSAC

In this example, we see how to robustly fit a linear model to faulty data using the RANSAC algorithm.

The ordinary linear regressor is sensitive to outliers, and the fitted line can easily be skewed away from the true underlying relationship of data.

The RANSAC regressor automatically splits the data into inliers and outliers, and the fitted line is determined only by the identified inliers.

    Estimated coefficients (true, linear regression, RANSAC):
    82.1903908407869 [54.17236387] [82.08533159]

    import numpy as np
    from matplotlib import pyplot as plt

    from sklearn import datasets, linear_model

    n_samples = 1000
    n_outliers = 50

    X, y, coef = datasets.make_regression(
        n_samples=n_samples,
        n_features=1,
        n_informative=1,
        noise=10,
        coef=True,
        random_state=0,
    )

    # Add outlier data
    np.random.seed(0)
    X[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))
    y[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)

    # Fit line using all data
    lr = linear_model.LinearRegression()
    lr.fit(X, y)

    # Robustly fit linear model with RANSAC algorithm
    ransac = linear_model.RANSACRegressor()
    ransac.fit(X, y)
    inlier_mask = ransac.inlier_mask_
    outlier_mask = np.logical_not(inlier_mask)

    # Predict data of estimated models
    line_X = np.arange(X.min(), X.max())[:, np.newaxis]
    line_y = lr.predict(line_X)
    line_y_ransac = ransac.predict(line_X)

    # Compare estimated coefficients
    print("Estimated coefficients (true, linear regression, RANSAC):")
    print(coef, lr.coef_, ransac.estimator_.coef_)

    lw = 2
    plt.scatter(
        X[inlier_mask], y[inlier_mask], color="yellowgreen", marker=".", label="Inliers"
    )
    plt.scatter(
        X[outlier_mask], y[outlier_mask], color="gold", marker=".", label="Outliers"
    )
    plt.plot(line_X, line_y, color="navy", linewidth=lw, label="Linear regressor")
    plt.plot(
        line_X,
        line_y_ransac,
        color="cornflowerblue",
        linewidth=lw,
        label="RANSAC regressor",
    )
    plt.legend(loc="lower right")
    plt.xlabel("Input")
    plt.ylabel("Response")
    plt.show()

Total running time of the script: (0 minutes 0.063 seconds)

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