使用python numpy矩阵类的梯度下降

Question

我试图用python实现一元梯度下降算法。我尝试了很多不同的方法，但都没用。下面是我尝试过的一个例子。我做错什么了？提前谢谢！！！在

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 

有一点更新；我以前尝试用一种更“矢量化”的方式来实现，比如：

^{pr2}$

这导致θ为[[-0.86221218]，[0.88827876]]。在

Answer 1

有两个问题，都与浮点有关：

1初始化θ矩阵如下：

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

2更改更新行，将(1/m)替换为(1.0/m)：

^{pr2}$

另一个无关的注意事项是：您的tempTheta变量是不必要的。在