用TensorFlow實現(xiàn)戴明回歸算法的示例

更新時間：2018年05月02日 11:27:56 作者：lilongsy

這篇文章主要介紹了用TensorFlow實現(xiàn)戴明回歸算法的示例，小編覺得挺不錯的，現(xiàn)在分享給大家，也給大家做個參考。一起跟隨小編過來看看吧

如果最小二乘線性回歸算法最小化到回歸直線的豎直距離（即，平行于y軸方向），則戴明回歸最小化到回歸直線的總距離（即，垂直于回歸直線）。其最小化x值和y值兩個方向的誤差，具體的對比圖如下圖。

線性回歸算法和戴明回歸算法的區(qū)別。左邊的線性回歸最小化到回歸直線的豎直距離；右邊的戴明回歸最小化到回歸直線的總距離。

線性回歸算法的損失函數(shù)最小化豎直距離；而這里需要最小化總距離。給定直線的斜率和截距，則求解一個點到直線的垂直距離有已知的幾何公式。代入幾何公式并使TensorFlow最小化距離。

損失函數(shù)是由分子和分母組成的幾何公式。給定直線y=mx+b，點（x0，y0），則求兩者間的距離的公式為：

# 戴明回歸
#----------------------------------
#
# This function shows how to use TensorFlow to
# solve linear Deming regression.
# y = Ax + b
#
# We will use the iris data, specifically:
# y = Sepal Length
# x = Petal Width

import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from sklearn import datasets
from tensorflow.python.framework import ops
ops.reset_default_graph()

# Create graph
sess = tf.Session()

# Load the data
# iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)]
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])

# Declare batch size
batch_size = 50

# Initialize placeholders
x_data = tf.placeholder(shape=[None, 1], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)

# Create variables for linear regression
A = tf.Variable(tf.random_normal(shape=[1,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))

# Declare model operations
model_output = tf.add(tf.matmul(x_data, A), b)

# Declare Demming loss function
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))

# Declare optimizer
my_opt = tf.train.GradientDescentOptimizer(0.1)
train_step = my_opt.minimize(loss)

# Initialize variables
init = tf.global_variables_initializer()
sess.run(init)

# Training loop
loss_vec = []
for i in range(250):
  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)
  if (i+1)%50==0:
    print('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))
    print('Loss = ' + str(temp_loss))

# Get the optimal coefficients
[slope] = sess.run(A)
[y_intercept] = sess.run(b)

# Get best fit line
best_fit = []
for i in x_vals:
 best_fit.append(slope*i+y_intercept)

# Plot the result
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.title('Sepal Length vs Pedal Width')
plt.xlabel('Pedal Width')
plt.ylabel('Sepal Length')
plt.show()

# Plot loss over time
plt.plot(loss_vec, 'k-')
plt.title('L2 Loss per Generation')
plt.xlabel('Generation')
plt.ylabel('L2 Loss')
plt.show()

結(jié)果：