Tensorflow is more than just a deep learning framework. It is a general computation framework to perform general mathematical operations in a parallel and distributed manner. An example of such is described below.

A basic statistical example that is commonly utilized and is rather simple to compute is fitting a line to a dataset. The method to do so in tensorflow is described below in code and comments.

The main steps of the (TensorFlow) script are:

- Declare placeholders (
`x_ph`

,`y_ph`

) and variables (`W`

,`b`

) - Define the initialization operator (
`init`

) - Declare operations on the placeholders and variables (
`y_pred`

,`loss`

,`train_op`

) - Create a session (
`sess`

) - Run the initialization operator (
`sess.run(init)`

) - Run some graph operations (e.g.
`sess.run([train_op, loss], feed_dict={x_ph: x, y_ph: y})`

)

The graph construction is done using the Python TensorFlow API (could also be done using the C++ TensorFlow API). Running the graph will call low-level C++ routines.

```
'''
function: create a linear model which try to fit the line
y = x + 2 using SGD optimizer to minimize
root-mean-square(RMS) loss function
'''
import tensorflow as tf
import numpy as np
# number of epoch
num_epoch = 100
# training data x and label y
x = np.array([0., 1., 2., 3.], dtype=np.float32)
y = np.array([2., 3., 4., 5.], dtype=np.float32)
# convert x and y to 4x1 matrix
x = np.reshape(x, [4, 1])
y = np.reshape(y, [4, 1])
# test set(using a little trick)
x_test = x + 0.5
y_test = y + 0.5
# This part of the script builds the TensorFlow graph using the Python API
# First declare placeholders for input x and label y
# Placeholders are TensorFlow variables requiring to be explicitly fed by some
# input data
x_ph = tf.placeholder(tf.float32, shape=[None, 1])
y_ph = tf.placeholder(tf.float32, shape=[None, 1])
# Variables (if not specified) will be learnt as the GradientDescentOptimizer
# is run
# Declare weight variable initialized using a truncated_normal law
W = tf.Variable(tf.truncated_normal([1, 1], stddev=0.1))
# Declare bias variable initialized to a constant 0.1
b = tf.Variable(tf.constant(0.1, shape=[1]))
# Initialize variables just declared
init = tf.initialize_all_variables()
# In this part of the script, we build operators storing operations
# on the previous variables and placeholders.
# model: y = w * x + b
y_pred = x_ph * W + b
# loss function
loss = tf.mul(tf.reduce_mean(tf.square(tf.sub(y_pred, y_ph))), 1. / 2)
# create training graph
train_op = tf.train.GradientDescentOptimizer(0.1).minimize(loss)
# This part of the script runs the TensorFlow graph (variables and operations
# operators) just built.
with tf.Session() as sess:
# initialize all the variables by running the initializer operator
sess.run(init)
for epoch in xrange(num_epoch):
# Run sequentially the train_op and loss operators with
# x_ph and y_ph placeholders fed by variables x and y
_, loss_val = sess.run([train_op, loss], feed_dict={x_ph: x, y_ph: y})
print('epoch %d: loss is %.4f' % (epoch, loss_val))
# see what model do in the test set
# by evaluating the y_pred operator using the x_test data
test_val = sess.run(y_pred, feed_dict={x_ph: x_test})
print('ground truth y is: %s' % y_test.flatten())
print('predict y is : %s' % test_val.flatten())
```

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