python - Numpy 和 TensorFlow 之间的差异

Question

我正在尝试编写两个脚本来演示局部加权线性回归。我在第一个脚本中使用 Numpy 来解决矩阵问题，如下所示:

trX = np.linspace(0, 1, 100) 
trY= trX + np.random.normal(0,1,100)
xArr = []
yArr = []
for i in range(len(trX)):
    xArr.append([1.0,float(trX[i])])
    yArr.append(float(trY[i]))
xMat = mat(xArr); 
yMat = mat(yArr).T
m = shape(xMat)[0]
weights = mat(eye((m)))
k = 0.01
yHat = zeros(m)

for i in range(m):
    for j in range(m):
        diffMat = xArr[i] - xMat[j,:]
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))
    xTx = xMat.T * (weights * xMat)
    if linalg.det(xTx) == 0.0:
        print("This matrix is singular, cannot do inverse")
    ws = xTx.I * (xMat.T * (weights * yMat))
    yHat[i] = xArr[i]*ws


plt.scatter(trX, trY) 

plt.plot(trX, yHat, 'r')
plt.show() 

如果运行上面的脚本，结果:

在第二个脚本中，我使用了 TensorFlow 来解决矩阵问题。该脚本如下所示:

trX = np.linspace(0, 1, 100) 
trY= trX + np.random.normal(0,1,100)

sess = tf.Session()
xArr = []
yArr = []
for i in range(len(trX)):
    xArr.append([1.0,float(trX[i])])
    yArr.append(float(trY[i]))

xMat = mat(xArr); 
yMat = mat(yArr).T

A_tensor = tf.constant(xMat)
b_tensor = tf.constant(yMat)

m = shape(xMat)[0]
weights = mat(eye((m)))
k = 0.01
yHat = zeros(m)
for i in range(m):
    for j in range(m):
        diffMat = xMat[i]- xMat[j,:]
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))
    weights_tensor = tf.constant(weights)
    # Matrix inverse solution
    wA = tf.matmul(weights_tensor, A_tensor)
    tA_A = tf.matmul(tf.transpose(A_tensor), wA)
    tA_A_inv = tf.matrix_inverse(tA_A)
    wb = tf.matmul(weights_tensor, b_tensor)
    tA_wb = tf.matmul(tf.transpose(A_tensor), wb)
    solution = tf.matmul(tA_A_inv, tA_wb)
    sol_val = sess.run(solution)
    yHat[i] =sol_val[0][0]*xArr[i][1] + sol_val[1][0] 

plt.scatter(trX, trY) 

plt.plot(trX, yHat, 'r')
plt.show() 

如果运行它:

两个结果之间有什么区别？或者也许我的脚本中有错误的东西？请帮助我。

Answer 1

问题出在代码行上，

yHat[i] =sol_val[0][0]*xArr[i][1] + sol_val[1][0] 

Numpy 数组乘法发生错误。

把上面这行代码换成

就可以正常工作了

yHat[i] =sol_val[0][0]*xArr[i][0] + sol_val[1][0]*xArr[i][1]

完整的工作代码如下:

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
from numpy import *

import tensorflow as tf

trX = np.linspace(0, 1, 100) 
trY= trX + np.random.normal(0,1,100)
#print('trY = ', trY)

sess = tf.Session()
xArr = []
yArr = []
for i in range(len(trX)):
    xArr.append([1.0,float(trX[i])])
    yArr.append(float(trY[i]))

xMat = mat(xArr); 
yMat = mat(yArr).T

A_tensor = tf.constant(xMat)
b_tensor = tf.constant(yMat)

#print("A_Tensor = xMat = ", sess.run(A_tensor))
#print("B_Tensor = yMat = ", sess.run(b_tensor))

m = shape(xMat)[0]
weights = mat(eye((m)))
k = 0.01
yHat = zeros(m)
for i in range(m):
    for j in range(m):
        diffMat = xMat[i]- xMat[j,:]
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))
    weights_tensor = tf.constant(weights)    
    # Matrix inverse solution
    wA = tf.matmul(weights_tensor, A_tensor)
    tA_A = tf.matmul(tf.transpose(A_tensor), wA)
    tA_A_inv = tf.matrix_inverse(tA_A)
    wb = tf.matmul(weights_tensor, b_tensor)
    tA_wb = tf.matmul(tf.transpose(A_tensor), wb)
    solution = tf.matmul(tA_A_inv, tA_wb)
    sol_val = sess.run(solution)
    #plt.plot(sol_val, 'b')
    #plt.show()
    #print("Sol_Val = ", sol_val)
    #print("Sol_Val[0][0] = ", sol_val[0][0])
    #print("Sol_Val[1][0] = ", sol_val[1][0])
    #print('xArr[i] = ', np.array(xArr[i]))
    #print('xArr[i][0] = ', np.array(xArr[i][0]))
    #print('xArr[i][1] = ', np.array(xArr[i][1]))
    #yHat[i] =sol_val[0][0]*xArr[i][1] + sol_val[1][0]
    yHat[i] =sol_val[0][0]*xArr[i][0] + sol_val[1][0]*xArr[i][1]
    #print("Weights = ", sess.run(weights_tensor))
    #yHat[i] = np.array(xArr[i])*sol_val
    #print(sol_val)

plt.scatter(trX, trY) 

plt.plot(trX, yHat, 'r')
plt.show()

剧情如下图所示: