我正在尝试编写两个演示局部加权线性回归的脚本。在第一个脚本中，我使用Numpy来解决矩阵问题，代码如下：

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).Tm = shape(xMat)[0]weights = mat(eye((m)))k = 0.01yHat = 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]*wsplt.scatter(trX, trY) plt.plot(trX, yHat, 'r')plt.show() 

运行上述脚本后，得到的结果如下：

在第二个脚本中，我使用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).TA_tensor = tf.constant(xMat)b_tensor = tf.constant(yMat)m = shape(xMat)[0]weights = mat(eye((m)))k = 0.01yHat = 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() 

运行后，得到的结果如下：

导致两种结果不同的原因是什么？或者我的脚本中是否有错误的地方？请帮帮我。

回答：

问题出在代码的这一行，

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

Numpy数组乘法计算不正确。

如果将上述代码行替换为以下内容，将会正常工作

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 npimport tensorflow as tfimport matplotlib.pyplot as pltfrom numpy import *import tensorflow as tftrX = 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).TA_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 = 0.01yHat = 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()

下图显示了结果：