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Lasso 在密集和稀疏数据上的应用#
我们展示了 linear_model.Lasso 在密集和稀疏数据上提供相同的结果，并且在稀疏数据的情况下速度有所提高。
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
from time import time
from scipy import linalg, sparse
from sklearn.datasets import make_regression
from sklearn.linear_model import Lasso
比较密集数据上的两种 Lasso 实现#
我们创建了一个适合 Lasso 的线性回归问题，即具有比样本更多的特征。然后，我们将数据矩阵存储为密集格式（常规）和稀疏格式，并在每种格式上训练一个 Lasso 模型。我们计算两者的运行时间，并通过计算它们学习到的系数之间差异的欧几里得范数来检查它们是否学习了相同的模型。由于数据是密集的，我们期望使用密集数据格式能获得更好的运行时间。
X, y = make_regression(n_samples=200, n_features=5000, random_state=0)
# create a copy of X in sparse format
X_sp = sparse.coo_matrix(X)
alpha = 1
sparse_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=1000)
dense_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=1000)
t0 = time()
sparse_lasso.fit(X_sp, y)
print(f"Sparse Lasso done in {(time() - t0):.3f}s")
t0 = time()
dense_lasso.fit(X, y)
print(f"Dense Lasso done in {(time() - t0):.3f}s")
# compare the regression coefficients
coeff_diff = linalg.norm(sparse_lasso.coef_ - dense_lasso.coef_)
print(f"Distance between coefficients : {coeff_diff:.2e}")
#
Sparse Lasso done in 0.101s
Dense Lasso done in 0.032s
Distance between coefficients : 5.09e-14
比较稀疏数据上的两种 Lasso 实现#
我们通过将所有小值替换为 0 来使前一个问题稀疏，并运行与上面相同的比较。由于数据现在是稀疏的，我们期望使用稀疏数据格式的实现更快。
# make a copy of the previous data
Xs = X.copy()
# make Xs sparse by replacing the values lower than 2.5 with 0s
Xs[Xs < 2.5] = 0.0
# create a copy of Xs in sparse format
Xs_sp = sparse.coo_matrix(Xs)
Xs_sp = Xs_sp.tocsc()
# compute the proportion of non-zero coefficient in the data matrix
print(f"Matrix density : {(Xs_sp.nnz / float(X.size) * 100):.3f}%")
alpha = 0.1
sparse_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=10000)
dense_lasso = Lasso(alpha=alpha, fit_intercept=False, max_iter=10000)
t0 = time()
sparse_lasso.fit(Xs_sp, y)
print(f"Sparse Lasso done in {(time() - t0):.3f}s")
t0 = time()
dense_lasso.fit(Xs, y)
print(f"Dense Lasso done in {(time() - t0):.3f}s")
# compare the regression coefficients
coeff_diff = linalg.norm(sparse_lasso.coef_ - dense_lasso.coef_)
print(f"Distance between coefficients : {coeff_diff:.2e}")
Matrix density : 0.626%
Sparse Lasso done in 0.144s
Dense Lasso done in 0.731s
Distance between coefficients : 4.22e-13
脚本总运行时间： (0 minutes 1.074 seconds)
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