使用python、numpy线性回归

线性回归的原理不再赘述，本文给出了一个简单的使用梯度下降的线性回归模拟。import numpy as np
def weightsUpdate(data,w,b,learning_rate=0.01):
for x0,y0 in data:
y=np.dot(x0,w)+b
w_gradient = (y - y0) * x0.T#求w的梯度
b_gradient=(y-y0)[0];#求b的梯度；取标量
w-=w_gradient*learning_rate#权值更新
b-=b_gradient
loss=0.5*np.square(y-y0)
return [w,b,loss[0][0]]

def generateData(w,b,dataNum=10):#根据w,b生成数据
data = []

for i in range(dataNum):
noise = np.random.randn(1) * 0.01
x0 = np.random.randn(1,w.shape[0])
y0 = np.dot(x0, w) + b+noise
x = [x0, y0]
data.append(x)
return data

def linearRegressionTrain(data):
w0=np.random.randn(data[0][0].shape[1],1)
b0=np.random.randn(1)
for i in range(1000):
w0, b0,loss = weightsUpdate(data, w0, b0,0.01)
if(i%100==0):
print(loss)

return [w0,b0]

#y=2*x1+3*x2+1
w=np.array([[2],[3],[4],[5]])
b=np.array([1])

data=generateData(w,b)
w0,b0=linearRegressionTrain(data)
print(" w=", w,'\n',"w0=", w0, '\n',"b=", b, '\n',"b0=", b0)

实现的比较简单，效果还不错