基于Tensorflow的戴明回归算法

1、戴明回归算法

戴明回归最小化，求的是点到回归直线的距离。具体是最小化x值和y值两个方向的误差。

2、Tensorflow实现戴明回归算法

（1）导入编程库，创建会话等

import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from sklearn import datasets

sess = tf.Session()
iris = datasets.load_iris()

x_vals = np.array([x[3] for x in iris.data])
y_vals = np.array([y[0] for y in iris.data])

learning_rate = 0.05
batch_size = 50
x_data = tf.placeholder(shape=[None,1], dtype = tf.float32)
y_target = tf.placeholder(shape =[None,1],dtype = tf.float32)

A = tf.Variable(tf.random_normal(shape=[1,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))

model_output = tf.add(tf.matmul(x_data,A),b)

（2） 定义损失函数，即点到直线的距离公式

d=|y0−(mx0+b)|m2+1−−−−−−√$$d=\frac{|y_0-(m{x}_0+b)|}{\sqrt{m^2+1}}$$

demming_numerator = tf.abs(tf.subtract(y_target, tf.add(tf.matmul(x_data,A),b)))
demming_denominator = tf.sqrt(tf.add(tf.square(A),1))

loss = tf.reduce_mean(tf.truediv(demming_numerator,demming_denominator))

(3) 初始化变量，声明优化器，遍历迭代

init = tf.global_variables_initializer()
sess.run(init)
my_opt = tf.train.GradientDescentOptimizer(learning_rate)
train_step = my_opt.minimize(loss)

loss_vec = []

for i  in range(2500):
    rand_index = np.random.choice(len(x_vals),size = batch_size)
    rand_x = np.transpose([x_vals[rand_index]])
    rand_y = np.transpose([y_vals[rand_index]])
    sess.run(train_step,feed_dict={x_data:rand_x,y_target:rand_y})
    temp_loss = sess.run(loss ,feed_dict={x_data:rand_x,y_target:rand_y})
    loss_vec.append(temp_loss)

(4)输出优化结构

[slope] = sess.run(A)
[y_intercept] = sess.run(b)

best_fit = []
for i in x_vals:
    best_fit.append(slope*i + y_intercept)    

plt.plot(x_vals,y_vals,'o',label='Data Points')
plt.plot(x_vals,best_fit,'r-',label='Best fit line',linewidth=3)
plt.legend(loc='upper left')
plt.show()
plt.plot(loss_vec,'k-')

5、运行结果