70 lines
2.1 KiB
Python
70 lines
2.1 KiB
Python
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"""
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==================================================
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Automatic Relevance Determination Regression (ARD)
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==================================================
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Fit regression model with ARD
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"""
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print __doc__
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import numpy as np
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import pylab as pl
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from scipy import stats
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from scikits.learn.linear_model import ARDRegression
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################################################################################
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# Generating simulated data with Gaussian weigthts
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### Parameters of the example
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np.random.seed(0)
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n_samples, n_features = 50, 100
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### Create gaussian data
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X = np.random.randn(n_samples, n_features)
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### Create weigts with a precision lambda_ of 4.
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lambda_ = 4.
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w = np.zeros(n_features)
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### Only keep 10 weights of interest
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relevant_features = np.random.randint(0, n_features, 10)
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for i in relevant_features:
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w[i] = stats.norm.rvs(loc=0, scale=1. / np.sqrt(lambda_))
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### Create noite with a precision alpha of 50.
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alpha_ = 50.
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noise = stats.norm.rvs(loc=0, scale=1. / np.sqrt(alpha_), size=n_samples)
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### Create the target
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y = np.dot(X, w) + noise
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################################################################################
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### Fit the ARD Regression
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clf = ARDRegression(compute_score = True)
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clf.fit(X, y)
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################################################################################
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### Plot the true weights, the estimated weights and the histogram of the
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### weights
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pl.figure()
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axe = pl.axes([0.1,0.6,0.8,0.325])
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axe.set_title("ARD - Weights of the model")
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axe.plot(clf.coef_, 'b-', label="Estimate")
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axe.plot(w, 'g-', label="Ground truth")
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axe.set_xlabel("Features")
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axe.set_ylabel("Values of the weights")
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axe.legend(loc=1)
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axe = pl.axes([0.1,0.1,0.45,0.325])
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axe.set_title("Histogram of the weights")
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axe.hist(clf.coef_, bins=n_features, log=True)
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axe.plot(clf.coef_[relevant_features],5*np.ones(len(relevant_features)),'ro',
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label="Relevant features")
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axe.set_ylabel("Features")
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axe.set_xlabel("Values of the weights")
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axe.legend(loc=1)
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axe = pl.axes([0.65,0.1,0.3,0.325])
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axe.set_title("Objective function")
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axe.plot(clf.scores_)
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axe.set_ylabel("Score")
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axe.set_xlabel("Iterations")
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pl.show()
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