使用多项式逻辑回归 + L1 进行 MNIST 分类#

在这里，我们对 MNIST 数字分类任务的子集拟合了具有 L1 惩罚的多项式逻辑回归。为此，我们使用了 SAGA 算法：当样本数量明显大于特征数量时，这是一种快速的求解器，并且能够对非光滑目标函数进行精细优化，这在使用 l1 惩罚的情况下就是这种情况。测试准确率达到 > 0.8，而权重向量保持_稀疏_，因此更容易_解释_。

请注意，此 l1 惩罚线性模型的准确率明显低于 l2 惩罚线性模型或非线性多层感知器模型在该数据集上所能达到的准确率。

Sparsity with L1 penalty: 74.57%
Test score with L1 penalty: 0.8253
Example run in 8.858 s

# Author: Arthur Mensch <[email protected]>
# License: 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("Class %i" % 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 8.938 秒）