《scikit-learn机器学习》波斯顿房价预测（线性回归预测）

本节内容：
首先是要导入数据，看数据有多少个样本，有多少个特征标签，对其进行模型训练，用线性回归的方式对80%的训练集进行训练，发现训练的score比较低，优化为多项式模型，画学习曲线判断哪个多项式最符合，然后就训练出房价。

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导入模块

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

导入数据并且看有多少样本

from sklearn.datasets import load_boston

boston = load_boston()
X = boston.data
y = boston.target
X.shape

看有多少特征标签

boston.feature_names

分离数据集

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=3)

用线性回归模型进行训练

python3.8的time中，clock被禁用了，改为：perf_counter()

import time
from sklearn.linear_model import LinearRegression

model = LinearRegression()

start = time.perf_counter() 
model.fit(X_train, y_train)

train_score = model.score(X_train, y_train)
cv_score = model.score(X_test, y_test)
print('elaspe: {0:.6f}; train_score: {1:0.6f}; cv_score: {2:.6f}'.format(time.perf_counter()-start, train_score, cv_score))

发现预测的效果不太好，优化模型

二阶多项式模型：degree=2

from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline

def polynomial_model(degree=1):
    polynomial_features = PolynomialFeatures(degree=degree,
                                             include_bias=False)
    linear_regression = LinearRegression(normalize=True)
    pipeline = Pipeline([("polynomial_features", polynomial_features),
                         ("linear_regression", linear_regression)])
    return pipeline

model = polynomial_model(degree=2)

start = time.perf_counter()
model.fit(X_train, y_train)

train_score = model.score(X_train, y_train)
cv_score = model.score(X_test, y_test)
print('elaspe: {0:.6f}; train_score: {1:0.6f}; cv_score: {2:.6f}'.format(time.perf_counter()-start, train_score, cv_score))

绘制学习曲线

degree = 1，2，3，也就是一阶，二阶，三阶
二阶的学习曲线交叉间距太大，说明需要更多的训练集

from common.utils import plot_learning_curve
from sklearn.model_selection import ShuffleSplit

cv = ShuffleSplit(n_splits=10, test_size=0.2, random_state=0)
plt.figure(figsize=(18, 4))
title = 'Learning Curves (degree={0})'
degrees = [1, 2, 3]

start = time.clock()
plt.figure(figsize=(18, 4), dpi=200)
for i in range(len(degrees)):
    plt.subplot(1, 3, i + 1)
    plot_learning_curve(plt, polynomial_model(degrees[i]), title.format(degrees[i]), X, y, ylim=(0.01, 1.01), cv=cv)

print('elaspe: {0:.6f}'.format(time.clock()-start))

如果为三阶

其中score为负数，说明这个过拟合过分了，不适合

其实线性回归的模型都差不多，代码都是一个样子的，只用换degree就行。