利用Scikit-learn库进行Logistic回归（训练数据）与分类预测（测试数据） （1）求取样本数为1000、噪声为0.1、0.3、0.5、0.8、1、1.5时的预测精度并画出预测精度随噪声的变化曲线。 （2）画出样本数为1000、噪声为0.3时的样本与分类界线。

首先，导入需要的库和函数：

import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt

然后，生成样本数据和噪声：

np.random.seed(0)

n_samples = 1000
X = np.random.randn(n_samples, 2)
y = (X[:, 0] + X[:, 1] > 0).astype(int)  # 分类标签

noises = [0.1, 0.3, 0.5, 0.8, 1, 1.5]

接着，定义训练和预测函数：

def train_and_predict(X_train, y_train, X_test, y_test):
    clf = LogisticRegression()
    clf.fit(X_train, y_train)
    return clf.score(X_test, y_test)

def plot_accuracy(noises, accuracies):
    plt.plot(noises, accuracies)
    plt.title('Accuracy vs Noise')
    plt.xlabel('Noise')
    plt.ylabel('Accuracy')
    plt.show()

def plot_boundary(X, y, clf):
    x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
    y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
    xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1),
                         np.arange(y_min, y_max, 0.1))
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    plt.contourf(xx, yy, Z, alpha=0.4)
    plt.scatter(X[:, 0], X[:, 1], c=y, alpha=0.8)
    plt.title('Boundary')
    plt.xlabel('X1')
    plt.ylabel('X2')
    plt.show()

最后，进行训练和预测，并画出图像：

for noise in noises:
    X_noisy = X + noise * np.random.randn(n_samples, 2)
    X_train, X_test, y_train, y_test = train_test_split(X_noisy, y, test_size=0.3)
    accuracy = train_and_predict(X_train, y_train, X_test, y_test)
    accuracies.append(accuracy)

plot_accuracy(noises, accuracies)

# 使用噪声为0.3的样本进行训练和预测，并画出样本和分类界线
X_noisy = X + 0.3 * np.random.randn(n_samples, 2)
X_train, X_test, y_train, y_test = train_test_split(X_noisy, y, test_size=0.3)
clf = LogisticRegression()
clf.fit(X_train, y_train)
plot_boundary(X_noisy, y, clf)

预测精度随噪声的变化曲线：


样本和分类界线：