Lasso 应用于密集和稀疏数据#

我们证明了 linear_model.Lasso 对密集和稀疏数据提供了相同的结果，并且在稀疏数据的情况下，速度得到了提高。

from time import time

from scipy import linalg, sparse

from sklearn.datasets import make_regression
from sklearn.linear_model import Lasso

比较两种 Lasso 实现对密集数据的处理#

我们创建一个适合 Lasso 的线性回归问题，也就是说，特征多于样本。然后，我们将数据矩阵存储为密集（通常）和稀疏格式，并在每种格式上训练 Lasso。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。因为数据是密集的，所以我们期望使用密集数据格式可以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 0.120s
Dense Lasso done in 0.045s
Distance between coefficients : 1.01e-13

比较两种 Lasso 实现对稀疏数据的处理#

我们通过将所有小值替换为 0 来使先前的问题变得稀疏，并运行与上述相同的比较。因为数据现在是稀疏的，所以我们期望使用稀疏数据格式的实现速度更快。

# 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 0.213s
Dense Lasso done in  0.949s
Distance between coefficients : 8.65e-12

脚本总运行时间：（0 分钟 1.427 秒）