69 lines
2.0 KiB
Python
69 lines
2.0 KiB
Python
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"""
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===========================================================
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Plot Ridge coefficients as a function of the regularization
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===========================================================
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Shows the effect of collinearity in the coefficients of an estimator.
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.. currentmodule:: sklearn.linear_model
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:class:`Ridge` Regression is the estimator used in this example.
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Each color represents a different feature of the
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coefficient vector, and this is displayed as a function of the
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regularization parameter.
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This example also shows the usefulness of applying Ridge regression
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to highly ill-conditioned matrices. For such matrices, a slight
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change in the target variable can cause huge variances in the
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calculated weights. In such cases, it is useful to set a certain
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regularization (alpha) to reduce this variation (noise).
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When alpha is very large, the regularization effect dominates the
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squared loss function and the coefficients tend to zero.
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At the end of the path, as alpha tends toward zero
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and the solution tends towards the ordinary least squares, coefficients
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exhibit big oscillations. In practise it is necessary to tune alpha
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in such a way that a balance is maintained between both.
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"""
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# Author: Fabian Pedregosa -- <fabian.pedregosa@inria.fr>
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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 import linear_model
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# X is the 10x10 Hilbert matrix
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X = 1.0 / (np.arange(1, 11) + np.arange(0, 10)[:, np.newaxis])
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y = np.ones(10)
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# %%
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# Compute paths
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# -------------
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n_alphas = 200
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alphas = np.logspace(-10, -2, n_alphas)
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coefs = []
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for a in alphas:
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ridge = linear_model.Ridge(alpha=a, fit_intercept=False)
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ridge.fit(X, y)
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coefs.append(ridge.coef_)
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# %%
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# Display results
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# ---------------
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ax = plt.gca()
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ax.plot(alphas, coefs)
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ax.set_xscale("log")
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ax.set_xlim(ax.get_xlim()[::-1]) # reverse axis
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plt.xlabel("alpha")
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plt.ylabel("weights")
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plt.title("Ridge coefficients as a function of the regularization")
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plt.axis("tight")
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plt.show()
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