线性回归(linear_regression)，多项式回归(polynomial regression)（Tensorflow实现）

#回归
import numpy as  np
import tensorflow as tf
import matplotlib.pyplot as plt

n_observations=100
xs=np.linspace(-3,3,n_observations)
ys=np.sin(xs)+np.random.uniform(-0.5,0.5,n_observations)
plt.scatter(xs,ys)
plt.show()

X=tf.placeholder(tf.float32,name='X')
Y=tf.placeholder(tf.float32,name='Y')

# just state these two parameters
W=tf.Variable(tf.random_normal([1]),name='weight')
b=tf.Variable(tf.random_normal([1]),name='bias')

Y_pred=tf.add(tf.multiply(X,W),b,name="y_pred")

loss=tf.square(Y-Y_pred,name='loss')

learning_rate=0.01
optimizer=tf.train.ProximalGradientDescentOptimizer(learning_rate).minimize(loss)

n_samples=xs.shape[0]

# inititalize these parameters.Only after this step, the para will have value
init=tf.global_variables_initializer()

with tf.Session() as sess:
sess.run(init)
writer=tf.summary.FileWriter('./graphs/linear_reg',sess.graph)

for i in range(50):
total_loss=0
for x,y in zip(xs,ys):
_,l=sess.run([optimizer,loss],feed_dict={X:x,Y:y})
total_loss+=l

if i%5 ==0:
print('Epoch:{0}: {1}'.format(l,total_loss/n_samples) )

writer.close();
# need run, and then  you can get the content of w and b
W,b=sess.run([W,b])
print(W,b)

print ("W:"+str(W[0]))
print ("b:"+str(b[0]))

plt.plot(xs,ys,'bo',label='Real data')
plt.plot(xs,xs*W+b,'r',label='Predicted data')
plt.legend()
plt.show()

#多项式回归
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt

n_observation=100
xs=np.linspace(-3,3,n_observation)
ys=np.sin(xs)+np.random.uniform(-0.5,0.5,n_observation)
plt.scatter(xs,ys)
plt.show()

X=tf.placeholder(tf.float32,name="X")
Y=tf.placeholder(tf.float32,name="Y")

W=tf.Variable(tf.random_uniform([1]),name="weights")
b=tf.Variable(tf.random_uniform([1]),name="bias")

Y_pred=tf.add(tf.multiply(X,W),b)

W_2=tf.Variable(tf.random_uniform([1]),name="weights_2")
Y_pred=tf.add(tf.multiply(tf.pow(X,2),W_2),Y_pred)
W_3=tf.Variable(tf.random_uniform([1]),name="weights_3")
Y_pred=tf.add(tf.multiply(tf.pow(X,2),W_3),Y_pred)

sample_num=xs.shape[0]
loss=tf.reduce_sum(tf.pow(Y_pred-Y,2))/sample_num

learning_rate=0.01
optimizer=tf.train.GradientDescentOptimizer(learning_rate).minimize(loss)

init=tf.global_variables_initializer()

with tf.Session() as sess:
sess.run(init)

writer=tf.summary.FileWriter('./graphs/polynomial_reg',sess.graph)

for i in range(1000):
total_loss=0
for x,y in zip(xs,ys):
_,l=sess.run([optimizer,loss],feed_dict={X:x,Y:y})
total_loss+=l
if i%20 ==0:
print ('epoch {0}: {1}'.format(i,total_loss/sample_num))

writer.close()

W, W_2, W_3, b=sess.run([W, W_2, W_3, b])
print(W, W_2, W_3, b)

print ("W:" + str(W[0]))
# print(W, b)

print ("W:" + str(W[0]))
print ("W_2:" + str(W_2[0]))
print ("W_3:" + str(W_3[0]))
print ("b:" + str(b[0]))

plt.plot(xs,ys,'bo',label='real_data')
plt.plot(xs,xs*W+np.power(xs,2)*W_2+np.power(xs,3)*W_3+b,'r',label='Predicted data')
plt.legend()
plt.show()