101 lines
2.3 KiB
Python
101 lines
2.3 KiB
Python
"""
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========================================
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Lasso and Elastic Net for Sparse Signals
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========================================
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Estimates Lasso and Elastic-Net regression models on a manually generated
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sparse signal corrupted with an additive noise. Estimated coefficients are
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compared with the ground-truth.
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"""
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# %%
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# Data Generation
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# ---------------------------------------------------
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn.metrics import r2_score
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np.random.seed(42)
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n_samples, n_features = 50, 100
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X = np.random.randn(n_samples, n_features)
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# Decreasing coef w. alternated signs for visualization
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idx = np.arange(n_features)
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coef = (-1) ** idx * np.exp(-idx / 10)
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coef[10:] = 0 # sparsify coef
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y = np.dot(X, coef)
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# Add noise
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y += 0.01 * np.random.normal(size=n_samples)
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# Split data in train set and test set
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n_samples = X.shape[0]
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X_train, y_train = X[: n_samples // 2], y[: n_samples // 2]
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X_test, y_test = X[n_samples // 2 :], y[n_samples // 2 :]
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# %%
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# Lasso
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# ---------------------------------------------------
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from sklearn.linear_model import Lasso
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alpha = 0.1
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lasso = Lasso(alpha=alpha)
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y_pred_lasso = lasso.fit(X_train, y_train).predict(X_test)
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r2_score_lasso = r2_score(y_test, y_pred_lasso)
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print(lasso)
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print("r^2 on test data : %f" % r2_score_lasso)
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# %%
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# ElasticNet
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# ---------------------------------------------------
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from sklearn.linear_model import ElasticNet
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enet = ElasticNet(alpha=alpha, l1_ratio=0.7)
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y_pred_enet = enet.fit(X_train, y_train).predict(X_test)
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r2_score_enet = r2_score(y_test, y_pred_enet)
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print(enet)
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print("r^2 on test data : %f" % r2_score_enet)
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# %%
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# Plot
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# ---------------------------------------------------
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m, s, _ = plt.stem(
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np.where(enet.coef_)[0],
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enet.coef_[enet.coef_ != 0],
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markerfmt="x",
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label="Elastic net coefficients",
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use_line_collection=True,
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)
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plt.setp([m, s], color="#2ca02c")
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m, s, _ = plt.stem(
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np.where(lasso.coef_)[0],
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lasso.coef_[lasso.coef_ != 0],
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markerfmt="x",
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label="Lasso coefficients",
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use_line_collection=True,
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)
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plt.setp([m, s], color="#ff7f0e")
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plt.stem(
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np.where(coef)[0],
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coef[coef != 0],
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label="true coefficients",
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markerfmt="bx",
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use_line_collection=True,
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)
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plt.legend(loc="best")
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plt.title(
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"Lasso $R^2$: %.3f, Elastic Net $R^2$: %.3f" % (r2_score_lasso, r2_score_enet)
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)
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plt.show()
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