Introduction to TensorFlow, fitting point by point

In this notebook, we introduce TensorFlow by fitting a line of the form y=m*x+b point by point. This is a derivation of Jared Ostmeyer's Naked Tensor code.

Load dependencies and set seeds for reproducibility



In [1]:

    
import numpy as np
np.random.seed(42)
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
import tensorflow as tf
tf.set_random_seed(42)

Create a very small data set



In [2]:

    
xs = [0., 1., 2., 3., 4., 5., 6., 7.] # feature (independent variable)
ys = [-.82, -.94, -.12, .26, .39, .64, 1.02, 1.] # labels (dependent variable)



In [3]:

    
fig, ax = plt.subplots()
_ = ax.scatter(xs, ys)

Define variables -- the model parameters we'll learn -- and initialize them with "random" values



In [4]:

    
m = tf.Variable(-0.5)
b = tf.Variable(1.0)

One single point at a time, define the error between the true label and the model's prediction of the label



In [5]:

    
total_error = 0.0
for x,y in zip(xs, ys):
    y_model = m*x + b
    total_error += (y-y_model)**2

Define optimizer as SSE-minimizing gradient descent



In [6]:

    
optimizer_operation = tf.train.GradientDescentOptimizer(learning_rate=0.01).minimize(total_error)

Define an operator that will initialize the graph with all available global variables



In [7]:

    
initializer_op = tf.global_variables_initializer()

With the computational graph designed, we initialize a session to execute it



In [8]:

    
with tf.Session() as sess:
    
    sess.run(initializer_op)
    
    n_epochs = 10
    
    for iteration in range(n_epochs):
        sess.run(optimizer_operation)
    
    slope, intercept = sess.run([m, b])



In [9]:

    
slope









    Out[9]:





-265.02151



In [10]:

    
intercept









    Out[10]:





-53.551777

Calculate the predicted model outputs given the inputs xs



In [11]:

    
y_hat = slope*np.array(xs) + intercept



In [12]:

    
pd.DataFrame(list(zip(ys, y_hat)), columns=['y', 'y_hat'])









    Out[12]:






  
    
      
      y
      y_hat
    
  
  
    
      0
      -0.82
      -53.551777
    
    
      1
      -0.94
      -318.573292
    
    
      2
      -0.12
      -583.594807
    
    
      3
      0.26
      -848.616322
    
    
      4
      0.39
      -1113.637836
    
    
      5
      0.64
      -1378.659351
    
    
      6
      1.02
      -1643.680866
    
    
      7
      1.00
      -1908.702381



In [13]:

    
fig, ax = plt.subplots()

ax.scatter(xs, ys)
x_min, x_max = ax.get_xlim()
y_min, y_max = intercept, intercept + slope*(x_max-x_min)

ax.plot([x_min, x_max], [y_min, y_max])
_ = ax.set_xlim([x_min, x_max])



In [ ]:

	y	y_hat
0	-0.82	-53.551777
1	-0.94	-318.573292
2	-0.12	-583.594807
3	0.26	-848.616322
4	0.39	-1113.637836
5	0.64	-1378.659351
6	1.02	-1643.680866
7	1.00	-1908.702381