MNIST分类（使用多项式逻辑回归 + L1）#

在这里，我们对 MNIST 数字分类任务的一个子集应用了带 L1 惩罚的多项式逻辑回归。为此，我们使用了 SAGA 算法：当样本数量远大于特征数量时，该求解器速度很快，并且能够精确优化非平滑目标函数（L1 惩罚就是这种情况）。测试准确率达到 > 0.8，同时权重向量保持 *稀疏*，因此更容易 *解释*。

请注意，此 L1 惩罚线性模型在此数据集上的准确率显著低于 L2 惩罚线性模型或非线性多层感知机模型所能达到的水平。

Sparsity with L1 penalty: 74.57%
Test score with L1 penalty: 0.8253
Example run in 8.029 s

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

import time

import matplotlib.pyplot as plt
import numpy as np

from sklearn.datasets import fetch_openml
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.utils import check_random_state

# Turn down for faster convergence
t0 = time.time()
train_samples = 5000

# Load data from https://www.openml.org/d/554
X, y = fetch_openml("mnist_784", version=1, return_X_y=True, as_frame=False)

random_state = check_random_state(0)
permutation = random_state.permutation(X.shape[0])
X = X[permutation]
y = y[permutation]
X = X.reshape((X.shape[0], -1))

X_train, X_test, y_train, y_test = train_test_split(
    X, y, train_size=train_samples, test_size=10000
)

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# Turn up tolerance for faster convergence
clf = LogisticRegression(C=50.0 / train_samples, penalty="l1", solver="saga", tol=0.1)
clf.fit(X_train, y_train)
sparsity = np.mean(clf.coef_ == 0) * 100
score = clf.score(X_test, y_test)
# print('Best C % .4f' % clf.C_)
print("Sparsity with L1 penalty: %.2f%%" % sparsity)
print("Test score with L1 penalty: %.4f" % score)

coef = clf.coef_.copy()
plt.figure(figsize=(10, 5))
scale = np.abs(coef).max()
for i in range(10):
    l1_plot = plt.subplot(2, 5, i + 1)
    l1_plot.imshow(
        coef[i].reshape(28, 28),
        interpolation="nearest",
        cmap=plt.cm.RdBu,
        vmin=-scale,
        vmax=scale,
    )
    l1_plot.set_xticks(())
    l1_plot.set_yticks(())
    l1_plot.set_xlabel(f"Class {i}")
plt.suptitle("Classification vector for...")

run_time = time.time() - t0
print("Example run in %.3f s" % run_time)
plt.show()

脚本总运行时间： (0 分 8.100 秒)

MNIST分类（使用多项式逻辑回归 + L1）#

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