API

from sklearn.linear_model import LinearRegression
# 获取数据
x = [
    [80,86],
    [82,80],
    [85,78],
    [90,90],
    [86,82],
    [82,90],
    [78,80],
    [92,84]
    
]
y = [84.2,80.6,80.1,90,83.2,87.6,79.4,93.4]
# 模型训练
# 实例化一个估计器
estimator = LinearRegression()
estimator.fit(x,y)
# 结果输出
print("线性回归的系数：\n",estimator.coef_)
print("预测结果：\n",estimator.predict([[100,80]]))

损失和优化

损失函数（预测点到实际点的距离的平方和）

优化算法

正规方程

正规方程推导

推导方式一

推导方式二

正规方程求解例子

梯度下降

由于存在多个极小值的情况，梯度下降不能保证取到最小值

梯度下降例子

单变量函数梯度下降

多变量函数梯度下降

梯度下降详细介绍

相关概念

推导过程

梯度算法种类

全梯度下降算法（FG）

随机梯度下降算法（SG）

小批量梯度下降算法（mini-batch）

随机平均梯度下降算法（SAG）

线性回归API

设 Y=kX+b，可以理解为，k：回归系数，b：偏执

总结对比

算法选择依据

波士顿房价预测案例

数据介绍

回归性能分析

代码实现

正规方程实现

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

获取数据

boston = load_boston()
boston

# 数据基本处理
x_train,x_test,y_train,y_test = train_test_split(boston.data,boston.target,test_size=0.2)
## 特征工程-标准化
transfer = StandardScaler()
x_train = transfer.fit_transform(x_train)
x_test = transfer.transform(x_test)

# 机器学习-线性回归
estimator = LinearRegression()
estimator.fit(x_train,y_train)

print("这个模型的偏置是:\n",estimator.intercept_)
print("这个模型的系数是:\n",estimator.coef_)

# 模型评估
y_pre = estimator.predict(x_test)
print("预测值是：\n",y_pre)

#  均方误差 
ret = mean_squared_error(y_test,y_pre)
print("均方误差：\n",ret)

梯度下降实现

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import SGDRegressor
from sklearn.metrics import mean_squared_error

获取数据

boston = load_boston()
boston

# 数据基本处理
x_train,x_test,y_train,y_test = train_test_split(boston.data,boston.target,test_size=0.2)
## 特征工程-标准化
transfer = StandardScaler()
x_train = transfer.fit_transform(x_train)
x_test = transfer.transform(x_test)

# 机器学习-线性回归
estimator = SGDRegressor(max_iter=1000)
estimator.fit(x_train,y_train)

print("这个模型的偏置是:\n",estimator.intercept_)
print("这个模型的系数是:\n",estimator.coef_)

# 模型评估
y_pre = estimator.predict(x_test)
print("预测值是：\n",y_pre)

#  均方误差 
ret = mean_squared_error(y_test,y_pre)
print("均方误差：\n",ret)

欠拟合和过拟合

原因及解决方法

正则化

正则化类别

Ridge Regression 岭回归

Lasso Regression Lasso 回归

Elastic Net 弹性网络

如何选择

Early Stopping（了解）

使用岭回归改进线性回归

API

Ridge（岭回归）代码实现

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import Ridge
from sklearn.metrics import mean_squared_error
# 获取数据
boston = load_boston()
# 数据基本处理
x_train,x_test,y_train,y_test = train_test_split(boston.data,boston.target,test_size=0.2)
## 特征工程-标准化
transfer = StandardScaler()
x_train = transfer.fit_transform(x_train)
x_test = transfer.transform(x_test)

# 机器学习-线性回归
estimator = Ridge(alpha=1.0)
estimator.fit(x_train,y_train)

print("这个模型的偏置是:\n",estimator.intercept_)
print("这个模型的系数是:\n",estimator.coef_)

# 模型评估
y_pre = estimator.predict(x_test)
print("预测值是：\n",y_pre)

#  均方误差 
ret = mean_squared_error(y_test,y_pre)
print("均方误差：\n",ret)

RidgeCV 代码实现

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import RidgeCV
from sklearn.metrics import mean_squared_error
# 获取数据
boston = load_boston()
# 数据基本处理
x_train,x_test,y_train,y_test = train_test_split(boston.data,boston.target,test_size=0.2)
## 特征工程-标准化
transfer = StandardScaler()
x_train = transfer.fit_transform(x_train)
x_test = transfer.transform(x_test)

# 机器学习-线性回归
estimator = RidgeCV(alphas=[0.1, 1.0, 10.0])
estimator.fit(x_train,y_train)


print("这个模型的偏置是:\n",estimator.intercept_)
print("这个模型的系数是:\n",estimator.coef_)

# 模型评估
y_pre = estimator.predict(x_test)
print("预测值是：\n",y_pre)

#  均方误差 
ret = mean_squared_error(y_test,y_pre)
print("均方误差：\n",ret)

sklearn模型保存和加载

API

案例

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import RidgeCV
from sklearn.metrics import mean_squared_error
from sklearn.externals import joblib


# 获取数据
boston = load_boston()
# 数据基本处理
x_train,x_test,y_train,y_test = train_test_split(boston.data,boston.target,test_size=0.2,random_state=22)
## 特征工程-标准化
transfer = StandardScaler()
x_train = transfer.fit_transform(x_train)
x_test = transfer.transform(x_test)

# 机器学习-线性回归
estimator = RidgeCV(alphas=[0.1, 1.0, 10.0])
estimator.fit(x_train,y_train)

# 模型保存
joblib.dump(estimator,"./test.pkl")


print("这个模型的偏置是:\n",estimator.intercept_)
print("这个模型的系数是:\n",estimator.coef_)

# 模型评估
y_pre = estimator.predict(x_test)
print("预测值是：\n",y_pre)

#  均方误差 
ret = mean_squared_error(y_test,y_pre)
print("均方误差：\n",ret)

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import RidgeCV
from sklearn.metrics import mean_squared_error
from sklearn.externals import joblib

# 获取模型
estimator = joblib.load("./test.pkl")

print("这个模型的偏置是:\n",estimator.intercept_)
print("这个模型的系数是:\n",estimator.coef_)

# 模型评估
y_pre = estimator.predict(x_test)
print("预测值是：\n",y_pre)

#  均方误差 
ret = mean_squared_error(y_test,y_pre)
print("均方误差：\n",ret)