python - 使用 python numpy 矩阵类的梯度下降

Question

我正在尝试在 python 中实现单变量梯度下降算法。我尝试了很多不同的方法，但没有任何效果。以下是我尝试过的一个示例。我究竟做错了什么？提前致谢!!!

from numpy import *

class LinearRegression:

  def __init__(self,data_file):
    self.raw_data_ref = data_file
    self.theta = matrix([[0],[0]])
    self.iterations = 1500
    self.alpha = 0.001


  def format_data(self):
    data = loadtxt(self.raw_data_ref, delimiter = ',')
    dataMatrix = matrix(data)
    x = dataMatrix[:,0]
    y = dataMatrix[:,1]
    m = y.shape[0]
    vec = mat(ones((m,1)))
    x = concatenate((vec,x),axis = 1)
    return [x, y, m]


  def computeCost(self, x, y, m):
    predictions = x*self.theta
    squaredErrorsMat = power((predictions-y),2)
    sse = squaredErrorsMat.sum(axis = 0)
    cost = sse/(2*m)
    return cost


  def descendGradient(self, x, y, m):
      for i in range(self.iterations):

          predictions = x*self.theta
          errors = predictions - y
          sumDeriv1 = (multiply(errors,x[:,0])).sum(axis = 0)
          sumDeriv2 = (multiply(errors,x[:,1])).sum(axis = 0)

          print self.computeCost(x,y,m)

          tempTheta = self.theta
          tempTheta[0] = self.theta[0] - self.alpha*(1/m)*sumDeriv1
          tempTheta[1] = self.theta[1] - self.alpha*(1/m)*sumDeriv2

          self.theta[0] = tempTheta[0]
          self.theta[1] = tempTheta[1]


      return self.theta



regressor = LinearRegression('ex1data1.txt')
output = regressor.format_data()
regressor.descendGradient(output[0],output[1],output[2])
print regressor.theta 

一点更新；我之前尝试以更“矢量化”的方式进行操作，如下所示:

def descendGradient(self, x, y, m):
  for i in range(self.iterations):

      predictions = x*self.theta
      errors = predictions - y

      sumDeriv1 = (multiply(errors,x[:,0])).sum(axis = 0)
      sumDeriv2 = (multiply(errors,x[:,1])).sum(axis = 0)

      gammaMat = concatenate((sumDeriv1,sumDeriv2),axis = 0)
      coeff = self.alpha*(1.0/m)
      updateMatrix = gammaMat*coeff
      print updateMatrix, gammaMat


      jcost  = self.computeCost(x,y,m)
      print jcost
      tempTheta = self.theta
      tempTheta = self.theta - updateMatrix
      self.theta = tempTheta

  return self.theta

这导致了 [[-0.86221218],[0.88827876]] 的 theta。

Answer 1

您有两个问题，都与浮点有关:

1. 像这样初始化你的 theta 矩阵:

self.theta = matrix([[0.0],[0.0]])

2. 更改更新行，将 (1/m) 替换为 (1.0/m):

tempTheta[0] = self.theta[0] - self.alpha*(1.0/m)*sumDeriv1
tempTheta[1] = self.theta[1] - self.alpha*(1.0/m)*sumDeriv2

不相关的说明:您的 tempTheta 变量是不必要的。