70 lines
2.0 KiB
Python
70 lines
2.0 KiB
Python
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"""
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==========================
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Non-negative least squares
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==========================
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In this example, we fit a linear model with positive constraints on the
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regression coefficients and compare the estimated coefficients to a classic
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linear regression.
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.metrics import r2_score
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# %%
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# Generate some random data
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np.random.seed(42)
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n_samples, n_features = 200, 50
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X = np.random.randn(n_samples, n_features)
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true_coef = 3 * np.random.randn(n_features)
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# Threshold coefficients to render them non-negative
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true_coef[true_coef < 0] = 0
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y = np.dot(X, true_coef)
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# Add some noise
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y += 5 * np.random.normal(size=(n_samples,))
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# %%
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# Split the data in train set and test set
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from sklearn.model_selection import train_test_split
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X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5)
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# %%
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# Fit the Non-Negative least squares.
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from sklearn.linear_model import LinearRegression
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reg_nnls = LinearRegression(positive=True)
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y_pred_nnls = reg_nnls.fit(X_train, y_train).predict(X_test)
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r2_score_nnls = r2_score(y_test, y_pred_nnls)
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print("NNLS R2 score", r2_score_nnls)
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# %%
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# Fit an OLS.
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reg_ols = LinearRegression()
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y_pred_ols = reg_ols.fit(X_train, y_train).predict(X_test)
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r2_score_ols = r2_score(y_test, y_pred_ols)
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print("OLS R2 score", r2_score_ols)
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# %%
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# Comparing the regression coefficients between OLS and NNLS, we can observe
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# they are highly correlated (the dashed line is the identity relation),
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# but the non-negative constraint shrinks some to 0.
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# The Non-Negative Least squares inherently yield sparse results.
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fig, ax = plt.subplots()
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ax.plot(reg_ols.coef_, reg_nnls.coef_, linewidth=0, marker=".")
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low_x, high_x = ax.get_xlim()
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low_y, high_y = ax.get_ylim()
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low = max(low_x, low_y)
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high = min(high_x, high_y)
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ax.plot([low, high], [low, high], ls="--", c=".3", alpha=0.5)
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ax.set_xlabel("OLS regression coefficients", fontweight="bold")
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ax.set_ylabel("NNLS regression coefficients", fontweight="bold")
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