基于Tensorflow的线性回归

• 用Tensorflow求逆矩阵
• 用Tensorflow实现矩阵分解
• 用Tensorflow实现线性回归
• 理解线性回归中的损失函数
• 用Tensorflow实现戴明回归(Deming Regression)
• 用Tensorflow实现Lasson回归和岭回归(Ridge Regression)
• 用Tensorflow实现弹性网络回归(Elastic Net Regression)
• 用Tensorflow实现逻辑回归
  

3.1用Tensorflow求逆矩阵

线性回归算法能表示Ax=b。这里主要解决的是用矩阵x来求解系数。

1. 导入库，初始化计算图，生成数据

   import tensorflow as tf
   import numpy as np
   import matplotlib.pyplot as plt
   
   sess = tf.Session()
   x_vals = np.linspace(0, 10, 100)
   y_vals = x_vals + np.random.normal(0, 1, 100)
   

2. 创建后续求逆方法所需要的矩阵，即创建A，和b
   A 是x_vals_column和ones_column的合并

   x_vals_column = np.transpose(np.matrix(x_vals))
   ones_column = np.transpose(np.matrix(np.repeat(1, 100)))
   A = np.column_stack((x_vals_column, ones_column))
   b = np.transpose(np.matrix(y_vals))
   

3. 将矩阵A，b转换成张量

   A_tensor = tf.constant(A)
   b_tensor = tf.constant(b)
   

4. 调用求逆矩阵函数matrix_inverse()

   tA_A = tf.matmul(tf.transpose(A_tensor), A_tensor)
   tA_A_inv = tf.matrix_inverse(tA_A)
   product = tf.matmul(tA_A_inv, tf.transpose(A_tensor))
   solution = tf.matmul(product, b_tensor)
   solution_eval = sess.run(solution)
   

5. 从解中抽离系数，斜率和y截距

   slope = solution_eval[0][0]
   y_intercept = solution_eval[1][0]
   print('slope: ' + str(slope))
   print('y_intercept: ' + str(y_intercept))
   

6. 画出对应的图像

   best_fit = []
   for i in x_vals:
       best_fit.append(slope*i + y_intercept)
   plt.plot(x_vals, y_vals, 'o', label='Data')
   plt.plot(x_vals, best_fit, 'r-', label="Best fit line", linewidth=3)
   plt.legend(loc='upper left')
   plt.show()
   

   

3.2用Tensorflow实现矩阵的分解

当矩阵较大时，使用上面的方法来进行求解逆矩阵是十分耗时的，可以使用cholesky函数来进行分解，然后再进行求解矩阵

1. 导入第三方库，创建计算图，生成数据集，获取矩阵A，b

   ops.reset_default_graph()
   sess = tf.Session()
   x_vals = np.linspace(0, 10, 100)
   y_vals = x_vals + np.random.normal(0, 1, 100)
   x_vals_column = np.transpose(np.matrix(x_vals))
   ones_column = np.transpose(np.matrix(np.repeat(1, 100)))
   A = np.column_stack((x_vals_column, ones_column))
   b = np.transpose(np.matrix(y_vals))
   A_tensor = tf.constant(A)
   b_tensor = tf.constant(b)
   

2. 找到方阵的cholesky矩阵分解

   tA_A = tf.matmul(tf.transpose(A_tensor), A_tensor)
   L = tf.cholesky(tA_A)
   tA_b = tf.matmul(tf.transpose(A_tensor), b)
   sol1 = tf.matrix_solve(L, tA_b)
   sol2 = tf.matrix_solve(tf.transpose(L), sol1)
   

3. 抽离系数，绘制图像

   solution_eval = sess.run(sol2)
   slope = solution_eval[0][0]
   y_intercept = solution_eval[1][0]
   print("slope: "+ str(slope))
   print("y_intercept: " + str(y_intercept))
   
   best_fit = []
   for i in x_vals:
       best_fit.append(slope*i+y_intercept)
   plt.plot(x_vals, y_vals, 'o', label='Data')
   plt.plot(x_vals, best_fit, 'r-', label="Best fit line", linewidth=3)
   plt.legend(loc='upper left')
   plt.show()
   
   

   

3.3用Tensorflow实现线性回归算法

这里使用iris数据集，将使用(x值代表花瓣的宽度，y值代表花瓣的长度)找到最优的直线

1. 导入第三方库，创建计算图，加载数据集

   from sklearn import datasets
   from tensorflow.python.framework import ops
   
   ops.reset_default_graph()
   sess = tf.Session()
   iris = datasets.load_iris()
   x_vals = np.array([x[3] for x in iris.data])
   y_vals = np.array([y[0]