65 lines
2.0 KiB
Python
65 lines
2.0 KiB
Python
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"""
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=======================================================
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HuberRegressor vs Ridge on dataset with strong outliers
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=======================================================
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Fit Ridge and HuberRegressor on a dataset with outliers.
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The example shows that the predictions in ridge are strongly influenced
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by the outliers present in the dataset. The Huber regressor is less
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influenced by the outliers since the model uses the linear loss for these.
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As the parameter epsilon is increased for the Huber regressor, the decision
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function approaches that of the ridge.
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"""
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# Authors: Manoj Kumar mks542@nyu.edu
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# License: BSD 3 clause
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.datasets import make_regression
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from sklearn.linear_model import HuberRegressor, Ridge
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# Generate toy data.
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rng = np.random.RandomState(0)
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X, y = make_regression(
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n_samples=20, n_features=1, random_state=0, noise=4.0, bias=100.0
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)
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# Add four strong outliers to the dataset.
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X_outliers = rng.normal(0, 0.5, size=(4, 1))
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y_outliers = rng.normal(0, 2.0, size=4)
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X_outliers[:2, :] += X.max() + X.mean() / 4.0
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X_outliers[2:, :] += X.min() - X.mean() / 4.0
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y_outliers[:2] += y.min() - y.mean() / 4.0
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y_outliers[2:] += y.max() + y.mean() / 4.0
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X = np.vstack((X, X_outliers))
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y = np.concatenate((y, y_outliers))
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plt.plot(X, y, "b.")
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# Fit the huber regressor over a series of epsilon values.
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colors = ["r-", "b-", "y-", "m-"]
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x = np.linspace(X.min(), X.max(), 7)
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epsilon_values = [1, 1.5, 1.75, 1.9]
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for k, epsilon in enumerate(epsilon_values):
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huber = HuberRegressor(alpha=0.0, epsilon=epsilon)
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huber.fit(X, y)
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coef_ = huber.coef_ * x + huber.intercept_
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plt.plot(x, coef_, colors[k], label="huber loss, %s" % epsilon)
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# Fit a ridge regressor to compare it to huber regressor.
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ridge = Ridge(alpha=0.0, random_state=0)
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ridge.fit(X, y)
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coef_ridge = ridge.coef_
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coef_ = ridge.coef_ * x + ridge.intercept_
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plt.plot(x, coef_, "g-", label="ridge regression")
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plt.title("Comparison of HuberRegressor vs Ridge")
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plt.xlabel("X")
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plt.ylabel("y")
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plt.legend(loc=0)
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plt.show()
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