87 lines
2.8 KiB
Python
87 lines
2.8 KiB
Python
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"""
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==============================
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Lasso on dense and sparse data
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==============================
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We show that linear_model.Lasso provides the same results for dense and sparse
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data and that in the case of sparse data the speed is improved.
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"""
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from time import time
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from scipy import linalg, sparse
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from sklearn.datasets import make_regression
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from sklearn.linear_model import Lasso
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# %%
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# Comparing the two Lasso implementations on Dense data
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# -----------------------------------------------------
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#
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# We create a linear regression problem that is suitable for the Lasso,
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# that is to say, with more features than samples. We then store the data
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# matrix in both dense (the usual) and sparse format, and train a Lasso on
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# each. We compute the runtime of both and check that they learned the
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# same model by computing the Euclidean norm of the difference between the
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# coefficients they learned. Because the data is dense, we expect better
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# runtime with a dense data format.
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X, y = make_regression(n_samples=200, n_features=5000, random_state=0)
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# create a copy of X in sparse format
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X_sp = sparse.coo_matrix(X)
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alpha = 1
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sparse_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=1000)
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dense_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=1000)
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t0 = time()
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sparse_lasso.fit(X_sp, y)
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print(f"Sparse Lasso done in {(time() - t0):.3f}s")
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t0 = time()
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dense_lasso.fit(X, y)
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print(f"Dense Lasso done in {(time() - t0):.3f}s")
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# compare the regression coefficients
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coeff_diff = linalg.norm(sparse_lasso.coef_ - dense_lasso.coef_)
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print(f"Distance between coefficients : {coeff_diff:.2e}")
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#
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# %%
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# Comparing the two Lasso implementations on Sparse data
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# ------------------------------------------------------
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#
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# We make the previous problem sparse by replacing all small values with 0
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# and run the same comparisons as above. Because the data is now sparse, we
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# expect the implementation that uses the sparse data format to be faster.
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# make a copy of the previous data
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Xs = X.copy()
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# make Xs sparse by replacing the values lower than 2.5 with 0s
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Xs[Xs < 2.5] = 0.0
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# create a copy of Xs in sparse format
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Xs_sp = sparse.coo_matrix(Xs)
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Xs_sp = Xs_sp.tocsc()
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# compute the proportion of non-zero coefficient in the data matrix
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print(f"Matrix density : {(Xs_sp.nnz / float(X.size) * 100):.3f}%")
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alpha = 0.1
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sparse_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=10000)
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dense_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=10000)
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t0 = time()
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sparse_lasso.fit(Xs_sp, y)
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print(f"Sparse Lasso done in {(time() - t0):.3f}s")
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t0 = time()
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dense_lasso.fit(Xs, y)
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print(f"Dense Lasso done in {(time() - t0):.3f}s")
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# compare the regression coefficients
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coeff_diff = linalg.norm(sparse_lasso.coef_ - dense_lasso.coef_)
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print(f"Distance between coefficients : {coeff_diff:.2e}")
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# %%
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