线性回归实战-优快云博客

导包

import numpy as np

import matplotlib.pyplot as plt
%matplotlib inline

from sklearn.linear_model import LinearRegression#导入算法

创建数据

X = np.linspace(2,10,20).reshape(-1,1)

# f(x) = wx + b
y = np.random.randint(1,6,size = 1)*X + np.random.randint(-5,5,size = 1)

# 噪声，加盐
y += np.random.randn(20,1)*0.8

plt.scatter(X,y,color =  'red')

使用已有的线性回归拟合函数

lr = LinearRegression()
lr.fit(X,y)

w = lr.coef_[0,0]
b = lr.intercept_[0]
print(w,b)

plt.scatter(X,y)

x = np.linspace(1,11,50)

plt.plot(x,w*x + b,color = 'green')

自己实现线性回归

# 使用梯度下降解决一元一次的线性问题：w，b
class LinearModel(object):
    def __init__(self):#初始化方法
        self.w = np.random.randn(1)[0]
        self.b = np.random.randn(1)[0]
#     数学建模：将数据X和目标值关系用数学公式表达
    def model(self,x):#model 模型，f(x) = wx + b
        return self.w*x + self.b
    def loss(self,x,y):#最小二乘法
        cost = (y - self.model(x))**2
#         梯度就是偏导数，求解两个未知数：w，b
        gradient_w = 2*(y - self.model(x))*(-x)
        gradient_b = 2*(y - self.model(x))*(-1)
        return cost,gradient_w,gradient_b
#     梯度下降
    def gradient_descent(self,gradient_w,gradient_b,learning_rate = 0.1):
#         更新w，b
        self.w -= gradient_w*learning_rate
        self.b -= gradient_b*learning_rate
#     训练fit
    def fit(self,X,y):
        count = 0 #算法执行优化了3000次，退出
        tol = 0.0001
        
        last_w = self.w + 0.1
        last_b = self.b + 0.1
        length = len(X)
        while True:
            if count > 3000:#执行的次数到了
                break
#           求解的斜率和截距的精确度达到要求
            if (abs(last_w - self.w) < tol) and (abs(last_b - self.b) < tol):
                break
            cost = 0
            gradient_w = 0
            gradient_b = 0
            for i in range(length):
                cost_,gradient_w_,gradient_b_ = self.loss(X[i,0],y[i,0])
                cost += cost_/length
                gradient_w += gradient_w_/length
                gradient_b += gradient_b_/length
#             print('---------------------执行次数：%d。损失值是：%0.2f'%(count,cost))
            last_w = self.w
            last_b = self.b
            # 更新截距和斜率
            self.gradient_descent(gradient_w,gradient_b,0.01)
            count+=1
    def result(self):
        return self.w,self.b

使用自己实现的线性回归拟合函数

lm = LinearModel()

lm.fit(X,y)

w_,b_ = lm.result()
print(w_,b_)

plt.scatter(X,y,c = 'red')

plt.plot(x,3.1485*x -1.9334,color = 'green')

plt.plot(x,w*x + b,color = 'blue')

plt.title('自定义的算法拟合曲线',fontproperties = 'KaiTi')