【Python机器学习】实验02 线性回归

plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签
plt.rcParams['axes.unicode_minus']=False #用来正常显示负号

#可视化人口与收益之间的关系
data.plot(kind="scatter",x="人口",y="收益")
plt.xlabel("人口",fontsize=10)
plt.ylabel("收益",fontsize=10)
plt.title("人口与收益之间的关系")

col_num=data.shape[1]
m=data.shape[0]
#训练集中的特征
X=data.iloc[:,:col_num-1]
#训练集中的标签
y=data.iloc[:,col_num-1]

#定义MSE损失，均方损失函数
def cost(X,y,w):
    temp=h(X,w)
    cost=np.sum(np.square(temp-y))/(2*m)
    return cost

def computeCost(X,y,w):
    inner = np.power(((X @ w) - y), 2)# (m,n) @ (n, 1) -> (n, 1)
#     return np.sum(inner)/(2 * len(X))
    return np.sum(inner) / (2*m)

array([[-17.592  ],
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       [-13.662  ],
       [-11.854  ],
       [ -6.8233 ],
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       [ -4.3483 ],
       [-12.     ],
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       [ -4.2959 ],
       [ -7.2029 ],
       [ -1.9869 ],
       [ -0.14454],
       [ -9.0551 ],
       [ -0.61705]])

#超参数为I，学习率alpha,对所有样本
def gradient_descent(X,y,w,iter_num,alpha):
    temp=np.zeros((col_num-1,1))
    cost_lst=[] 
    for i in range(iter_num):
        error=h(X,w)-y
        for j in range(col_num-1):
            incre=np.multiply(error.ravel(),X[:,j].ravel())
            temp[j,0]=w[j,0]-((alpha/m)*np.sum(incre))
        w=temp
        cost_lst.append(cost(X,y,w))
    return w,cost_lst        

x=np.linspace(data["人口"].min(),data["人口"].max(),50)
y1=w[0,0]*1+w[1,0]*x
plt.plot(x,y1,"r-+",label="预测线")
plt.scatter(data["人口"],data["收益"], label='训练数据')
plt.xlabel("人口",fontsize=10)
plt.ylabel("收益",fontsize=10)
plt.title("人口与收益之间的关系")
plt.show()

import sklearn
from sklearn import linear_model
reg=linear_model.LinearRegression()
reg.fit(X,y)
reg.coef_

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       [  1.97357374]])

data2.insert(0,"ones",1)
col_num2=data2.shape[1]
m2=data2.shape[0]
X2=data2.iloc[:,:-1].values
y2=data2.iloc[:,-1].values.reshape((data2.shape[0],1))
w2=np.zeros((X2.shape[1],1))

#定义MSE损失，均方损失函数
def cost2(X,y,w):
    temp=h(X,w)
    cost=np.sum(np.square(temp-y))/(2*m2)
    return cost
#超参数为I，学习率alpha,对所有样本
def gradient_descent(X,y,w,iter_num,alpha):
    temp=np.zeros((col_num2-1,1))
    cost_lst=[] 
    for i in range(iter_num):
        error=h(X,w)-y
        for j in range(col_num2-1):
            incre=np.multiply(error.ravel(),X[:,j].ravel())
            temp[j,0]=w[j,0]-((alpha/m2)*np.sum(incre))
        w=temp
        cost_lst.append(cost2(X,y,w))
    return w,cost_lst        

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def lsm(X,y):
    w=np.linalg.inv(X.T@X)@X.T@y
    return w

def lsm_v(X,y):
    w=np.linalg.inv(np.dot(X.T,X))
    w=np.dot(w,X.T)
    w=np.dot(w,y)
    return w

#回到单变量的线性回归中来
x=X
y_1=reg.predict(x)
plt.plot(x,y_1,"r-+",label="预测线")
plt.scatter(data["人口"],data["收益"], label='训练数据')
plt.xlim(4.7,10)
plt.xlabel("人口",fontsize=10)
plt.ylabel("收益",fontsize=10)
plt.title("人口与收益之间的关系")
plt.show()

#回到单变量的线性回归中来,Ridge
x=X
y_1=reg_rigde.predict(x)
plt.plot(x,y_1,"r-+",label="预测线")
plt.scatter(data["人口"],data["收益"], label='训练数据')
plt.xlim(4.7,10)
plt.xlabel("人口",fontsize=10)
plt.ylabel("收益",fontsize=10)
plt.title("人口与收益之间的关系")
plt.show()

#回到单变量的线性回归中来,Lasso
x=X
y_1=reg_lasso.predict(x)
plt.plot(x,y_1,"r-+",label="预测线")
plt.scatter(data["人口"],data["收益"], label='训练数据')
plt.xlim(4.7,10)
plt.xlabel("人口",fontsize=10)
plt.ylabel("收益",fontsize=10)
plt.title("人口与收益之间的关系")
plt.show()

#超参数为I，学习率alpha,对所有样本
def gradient_descent_l2(X,y,w,iter_num,alpha,lambd):
    temp=np.zeros((col_num-1,1))
    cost_lst=[] 
    for i in range(iter_num):
        error=h(X,w)-y
        for j in range(col_num-1):
            incre=np.multiply(error.ravel(),X[:,j].ravel())
            temp[j,0]=w[j,0]-((alpha/m)*(np.sum(incre)+2*lambd*w[j,0]))
        w=temp
        cost_lst.append(cost(X,y,w))      
    return w,cost_lst  

iter_num=200
alpha=0.001
lambd=2
w=np.zeros((col_num-1,1))
w,cost_lst=gradient_descent_l2(X,y,w,iter_num,alpha,lambd)

plt.plot(range(iter_num),cost_lst,"r-+")
plt.xlabel("迭代次数")
plt.ylabel("误差")
plt.show()