# A linear regression learning algorithm example using TensorFlow library.

Linear regression model is one of the simplest regression models. It assumes linear relationship between X and Y. The output equation is defined as follows: $$\hat{y} = WX + b$$



In [1]:

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
%matplotlib inline




In [2]:

#  Training Parameters
learning_rate = 1e-1
training_epochs = 2000
display_step = 200




In [3]:

# textbook by Gareth James, Robert Tibshirani, and Trevor Hastie
import numpy as np
train_X = data[['TV']].values

train_Y = data.Sales.values
train_Y = train_Y[:,np.newaxis]

n_samples = train_X.shape[0]
print n_samples
print train_X.shape, train_Y.shape
plt.plot(train_X, train_Y, 'ro', label='Original data')
plt.show()




200
(200, 1) (200, 1)




In [4]:

import tensorflow as tf
# Define tf Graph Inputs
X = tf.placeholder("float",[None,1])
y = tf.placeholder("float",[None,1])

# Create Model variables
# Set model weights
W = tf.Variable(np.random.randn(), name="weight")
b = tf.Variable(np.random.randn(), name="bias")

# Construct a linear model




In [5]:

# Minimize the squared errors
cost = tf.reduce_sum(tf.pow(y_pred-y,2))/(2*n_samples) #L2 loss

# Define the optimizer




In [6]:

# Add summary ops to collect data
w_hist = tf.histogram_summary("weights", W)
b_hist = tf.histogram_summary("biases", b)
y_hist = tf.histogram_summary("y", y_pred)

cost_summary = tf.scalar_summary("cost", cost)

# Merge all the summaries and write them out to /tmp/linear_regression
merged = tf.merge_all_summaries()




In [7]:

# Initializing the variables
init = tf.initialize_all_variables()
# Launch the graph
with tf.Session() as sess:
writer = tf.train.SummaryWriter("tmp/linear_regression", sess.graph)

sess.run(init)

# Fit all training data
for epoch in range(training_epochs):
result = sess.run([optimizer, cost, merged], feed_dict={X: train_X, y: train_Y})
summary_str = result[2]

#Display logs per epoch step
if epoch % display_step == 0:
print "Epoch:", '%04d' % (epoch+1), "cost=", \
"{:.9f}".format(sess.run(cost, feed_dict={X: train_X, y:train_Y})), \
"W=", sess.run(W), "b=", sess.run(b)

print "Optimization Finished!"
print "cost=", sess.run(cost, feed_dict={X: train_X, y: train_Y}), \
"W=", sess.run(W), "b=", sess.run(b)

#Graphic display
plt.plot(train_X, train_Y, 'ro', label='Original data')
plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
plt.legend()
plt.show()




Epoch: 0001 cost= 7559.149414062 W= 0.796873 b= 1.67981
Epoch: 0201 cost= 8.403744698 W= 0.072892 b= 2.04738
Epoch: 0401 cost= 6.728885651 W= 0.0648825 b= 3.62269
Epoch: 0601 cost= 5.776206493 W= 0.0578431 b= 5.00651
Epoch: 0801 cost= 5.396698475 W= 0.0528921 b= 5.97979
Epoch: 1001 cost= 5.285205841 W= 0.0499658 b= 6.55506
Epoch: 1201 cost= 5.260797024 W= 0.0484924 b= 6.84472
Epoch: 1401 cost= 5.256837368 W= 0.0478597 b= 6.96909
Epoch: 1601 cost= 5.256369114 W= 0.0476293 b= 7.01438
Epoch: 1801 cost= 5.256329536 W= 0.0475588 b= 7.02823
Optimization Finished!
cost= 5.25633 W= 0.047541 b= 7.03173




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