In [1]:

    

import tensorflow as tf
import numpy as np
from matplotlib import animation
import matplotlib.pyplot as plt
from IPython.display import HTML
import seaborn as sns
import pandas as pd
from itertools import combinations_with_replacement
sns.set()
df = pd.read_csv('TempLinkoping2016.csv')
df.head()


    

    
Out[1]:







  

    

      

      
time
      
temp
    
  
  

    

      
0
      
0.002732
      
0.1
    
    

      
1
      
0.005464
      
-4.5
    
    

      
2
      
0.008197
      
-6.3
    
    

      
3
      
0.010929
      
-9.6
    
    

      
4
      
0.013661
      
-9.9
    
  

In [2]:

    

X = df.iloc[:, 0:1].values
Y = df.iloc[:, 1:2].values


    

In [3]:

    

n_features = X.shape[1]
degree = 15
combs = [combinations_with_replacement(range(n_features), i) for i in range(0, degree + 1)]
flat_combs = [item for sublist in combs for item in sublist]
X_new = np.empty((X.shape[0], len(flat_combs)))
for i, index_combs in enumerate(flat_combs):
    X_new[:, i] = np.prod(X[:, index_combs], axis=1)


    

In [4]:

    

class Polynomial:
    def __init__(self, learning_rate):
        self.X = tf.placeholder(tf.float32, (None, X_new.shape[1]))
        self.Y = tf.placeholder(tf.float32, (None, 1))
        w = tf.Variable(tf.random_normal([X_new.shape[1], 1]))
        b = tf.Variable(tf.random_normal([1]))
        self.logits = tf.matmul(self.X, w) + b
        self.cost = tf.reduce_mean(tf.square(self.Y - self.logits))
        self.optimizer = tf.train.AdamOptimizer(learning_rate).minimize(self.cost)


    

In [5]:

    

tf.reset_default_graph()
sess = tf.InteractiveSession()
model = Polynomial(3)
sess.run(tf.global_variables_initializer())
for i in range(1000):
    cost, _ = sess.run([model.cost, model.optimizer], feed_dict={model.X:X_new, model.Y:Y})
    if (i+1) % 100 == 0:
        print('epoch %d, MSE: %f'%(i+1, cost))


    

    




epoch 100, MSE: 12.724812
epoch 200, MSE: 12.150353
epoch 300, MSE: 11.931046
epoch 400, MSE: 11.810099
epoch 500, MSE: 11.745957
epoch 600, MSE: 11.706048
epoch 700, MSE: 11.674370
epoch 800, MSE: 11.645284
epoch 900, MSE: 11.617476
epoch 1000, MSE: 11.590941

In [6]:

    

y_output = sess.run(model.logits, feed_dict={model.X:X_new})
plt.scatter(X[:,0],Y[:,0])
plt.plot(X,y_output, c='red')
plt.show()


    

In [9]:

    

tf.reset_default_graph()
sess = tf.InteractiveSession()
model = Polynomial(3)
sess.run(tf.global_variables_initializer())

fig = plt.figure(figsize=(10,5))
ax = plt.axes()
ax.scatter(X[:,0],Y[:,0], c='b')
cost, y_output = sess.run([model.cost, model.logits], feed_dict={model.X:X_new, model.Y:Y})
ax.set_xlabel('epoch: %d, MSE: %f'%(0,cost))
line, = ax.plot(X,y_output, lw=2, c='r')

def gradient_mean_square(epoch):
    cost, y_output, _ = sess.run([model.cost, model.logits, model.optimizer], feed_dict={model.X:X_new, model.Y:Y})
    line.set_data(X,y_output)
    ax.set_xlabel('epoch: %d, MSE: %f'%(epoch,cost))
    return line, ax

anim = animation.FuncAnimation(fig, gradient_mean_square, frames=100, interval=200)
anim.save('animation-polynomial-regression.gif', writer='imagemagick', fps=10)


    

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