课后作业：广义线性模型¶

作者：欧新宇（Xinyu OU）

【作业提交】

将测试结果Excel电子表格形式进行提交，同时提交源代码。

测试结果命名为: ex04-结果-你的学号-你的姓名.xls (.xlsx)
源代码命名为: ex04-01-你的学号-你的姓名.py

*结果文件，要求每小题标注题号，两题之间要求空一行*

分别使用线性回归、岭回归及套索回归对"波士顿房价"数据集进行回归分析，要求：

在进行数据集划分的时候，训练集占70%，测试集占30%
分别测试岭回归 $alpha = [0, 0.1, 2, 5]$ 时的准确率
分别测试套索回归 $alpha = [0.001, 0.2, 1]$ 时的准确率
分别给出训练集和测试机的得分，要求结果保留4位小数 (ex04-01)

导入相关库

# 1.导入基本运算库
import numpy as np
import matplotlib.pyplot as plt

# 配置参数使 matplotlib绘图工具可以显示中文
plt.rcParams['font.sans-serif'] = [u'Microsoft YaHei']

# 2.导入线性回归模型
from sklearn.linear_model import LinearRegression
from sklearn.linear_model import Ridge
from sklearn.linear_model import Lasso
from sklearn.model_selection import train_test_split


# 3. 载入糖尿病情数据集，并使用train_test_split()函数对数据集进行划分
from sklearn.datasets import load_boston
X = load_boston().data
y = load_boston().target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state = 83, test_size = 0.3)

# 4. 训练模型
lr = LinearRegression().fit(X_train, y_train)
ridge0 = Ridge(alpha = 0).fit(X_train, y_train)
ridge01 = Ridge(alpha = 0.1).fit(X_train, y_train)
ridge2 = Ridge(alpha = 2).fit(X_train, y_train)
ridge5 = Ridge(alpha = 5).fit(X_train, y_train)
lasso001 = Lasso(alpha = 0.001, max_iter = 100000).fit(X_train, y_train)
lasso02 = Lasso(alpha = 0.2, max_iter = 100000).fit(X_train, y_train)
lasso1 = Lasso(alpha = 1, max_iter = 100000).fit(X_train, y_train)

# 4. 性能分析
print("线性回归：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(lr.score(X_train, y_train), lr.score(X_test, y_test)))
print("岭回归(alpha=0)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(ridge0.score(X_train, y_train), ridge0.score(X_test, y_test)))
print("岭回归(alpha=0.1)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(ridge01.score(X_train, y_train), ridge01.score(X_test, y_test)))
print("岭回归(alpha=2)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(ridge2.score(X_train, y_train), ridge2.score(X_test, y_test)))
print("岭回归(alpha=5)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(ridge5.score(X_train, y_train), ridge5.score(X_test, y_test)))
print("套索回归(alpha=0.001)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(lasso001.score(X_train, y_train), lasso001.score(X_test, y_test)))
print("套索回归(alpha=0.2)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(lasso02.score(X_train, y_train), lasso02.score(X_test, y_test)))
print("套索回归(alpha=1)：训练集得分: {0:.4f}，测试集得分: {1:.4f}".format(lasso1.score(X_train, y_train), lasso1.score(X_test, y_test)))

线性回归：训练集得分: 0.7469，测试集得分: 0.7129
岭回归(alpha=0)：训练集得分: 0.7469，测试集得分: 0.7129
岭回归(alpha=0.1)：训练集得分: 0.7468，测试集得分: 0.7138
岭回归(alpha=2)：训练集得分: 0.7404，测试集得分: 0.7143
岭回归(alpha=5)：训练集得分: 0.7362，测试集得分: 0.7123
套索回归(alpha=0.001)：训练集得分: 0.7469，测试集得分: 0.7131
套索回归(alpha=0.2)：训练集得分: 0.7232，测试集得分: 0.7069
套索回归(alpha=1)：训练集得分: 0.6793，测试集得分: 0.6261