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稠密和稀疏資料上的 Lasso#
我們顯示 linear_model.Lasso 對於稠密和稀疏資料提供相同的結果，並且在稀疏資料的情況下，速度會提高。
# 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
比較稠密資料上兩個 Lasso 實作#
我們建立適合 Lasso 的線性迴歸問題，也就是說，特徵比樣本多。然後，我們將資料矩陣以稠密 (一般的) 和稀疏格式儲存，並在每個矩陣上訓練 Lasso。我們計算兩者的執行時間，並透過計算它們所學習的係數之間的差的歐幾里得範數，檢查它們是否學習到相同的模型。由於資料是稠密的，我們預期稠密資料格式會獲得較佳的執行時間。
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 0.110s
Dense Lasso done in 0.038s
Distance between coefficients : 1.01e-13
比較稀疏資料上兩個 Lasso 實作#
我們透過將所有小值替換為 0 來使先前的問題變為稀疏，並執行與上述相同的比較。由於資料現在是稀疏的，我們預期使用稀疏資料格式的實作會更快。
# 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 0.200s
Dense Lasso done in 0.742s
Distance between coefficients : 8.65e-12
腳本的總執行時間：（0 分鐘 1.159 秒）
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