利用tensorflow实现线性回归（cholesky分解）

import matplotlib.pyplot as plt

import numpy as np

import tensorflow as tf

from tensorflow.python.framework import ops

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)

tA_A = tf.matmul(tf.transpose(A_tensor),A_tensor) #利用矩阵分解方法求解线性回归问题

L = tf.cholesky(tA_A) #cholesky 分解，返回的是下三角矩阵LL’x=b,返回L

#L 和L’是转置关系

tA_b = tf.matmul(tf.transpose(A_tensor),b)

sol1 = tf.matrix_solve(L,tA_b) # 利用tensorflow内置的方法解方程组

sol2 = tf.matrix_solve(tf.transpose(L),sol1)

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_fits = []

for i in x_vals:

best_fits.append(slope*i + y_intercept)

plt.plot(x_vals,y_vals,’^’,label=’Data’)

plt.plot(x_vals,best_fits,’-‘,color=’r’,label=’Best fit line’,linewidth=3)

plt.legend(loc=’upper left’)

plt.show()