python实现机器学习之多元线性回归

import numpy as np

def linearRegression(data_X,data_Y,learningRate,loopNum):
 W = np.zeros(shape=[1, data_X.shape[1]])
 # W的shape取决于特征个数，而x的行是样本个数，x的列是特征值个数
 # 所需要的W的形式为 行=特征个数，列=1 这样的矩阵。但也可以用1行，再进行转置：W.T
 # X.shape[0]取X的行数，X.shape[1]取X的列数
 b = 0

 #梯度下降
 for i in range(loopNum):
  W_derivative = np.zeros(shape=[1, data_X.shape[1]])
  b_derivative, cost = 0, 0

  WXPlusb = np.dot(data_X, W.T) + b # W.T：W的转置
  W_derivative += np.dot((WXPlusb - data_Y).T, data_X) # np.dot:矩阵乘法
  b_derivative += np.dot(np.ones(shape=[1, data_X.shape[0]]), WXPlusb - data_Y)
  cost += (WXPlusb - data_Y)*(WXPlusb - data_Y)
  W_derivative = W_derivative / data_X.shape[0] # data_X.shape[0]:data_X矩阵的行数，即样本个数
  b_derivative = b_derivative / data_X.shape[0]


  W = W - learningRate*W_derivative
  b = b - learningRate*b_derivative

  cost = cost/(2*data_X.shape[0])
  if i % 100 == 0:
   print(cost)
 print(W)
 print(b)

if __name__== "__main__":
 X = np.random.normal(0, 10, 100)
 noise = np.random.normal(0, 0.05, 20)
 W = np.array([[3, 5, 8, 2, 1]]) #设5个特征值
 X = X.reshape(20, 5)  #reshape成20行5列
 noise = noise.reshape(20, 1)
 Y = np.dot(X, W.T)+6 + noise
 linearRegression(X, Y, 0.003, 5000)

WXPlusb = np.dot(data_X, W.T) + b

W_derivative += np.dot((WXPlusb - data_Y).T, data_X)

b_derivative += np.dot(np.ones(shape=[1, data_X.shape[0]]), WXPlusb - data_Y)