Chapter 9 – Up and running with TensorFlow

This notebook contains all the sample code and solutions to the exercises in chapter 9.

Setup¶

First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:

In [1]:

# To support both python 2 and python 3
from __future__ import division, print_function, unicode_literals

# Common imports
import numpy as np
import os

# to make this notebook's output stable across runs
def reset_graph(seed=42):
    tf.reset_default_graph()
    tf.set_random_seed(seed)
    np.random.seed(seed)

# To plot pretty figures
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12

# Where to save the figures
PROJECT_ROOT_DIR = "."
CHAPTER_ID = "tensorflow"

def save_fig(fig_id, tight_layout=True):
    path = os.path.join(PROJECT_ROOT_DIR, "images", CHAPTER_ID, fig_id + ".png")
    print("Saving figure", fig_id)
    if tight_layout:
        plt.tight_layout()
    plt.savefig(path, format='png', dpi=300)

Creating and running a graph¶

In [2]:

import tensorflow as tf

reset_graph()

x = tf.Variable(3, name="x")
y = tf.Variable(4, name="y")
f = x*x*y + y + 2

In [3]:

Out[3]:

<tf.Tensor 'add_1:0' shape=() dtype=int32>

In [4]:

sess = tf.Session()
sess.run(x.initializer)
sess.run(y.initializer)
result = sess.run(f)
print(result)

In [5]:

sess.close()

In [6]:

with tf.Session() as sess:
    x.initializer.run()
    y.initializer.run()
    result = f.eval()

In [7]:

result

Out[7]:

In [8]:

init = tf.global_variables_initializer()

with tf.Session() as sess:
    init.run()
    result = f.eval()

In [9]:

result

Out[9]:

In [10]:

init = tf.global_variables_initializer()

In [11]:

sess = tf.InteractiveSession()
init.run()
result = f.eval()
print(result)

In [12]:

sess.close()

In [13]:

result

Out[13]:

Managing graphs¶

In [14]:

reset_graph()

x1 = tf.Variable(1)
x1.graph is tf.get_default_graph()

Out[14]:

True

In [15]:

graph = tf.Graph()
with graph.as_default():
    x2 = tf.Variable(2)

x2.graph is graph

Out[15]:

True

In [16]:

x2.graph is tf.get_default_graph()

Out[16]:

False

In [17]:

w = tf.constant(3)
x = w + 2
y = x + 5
z = x * 3

with tf.Session() as sess:
    print(y.eval())  # 10
    print(z.eval())  # 15

10
15

In [18]:

with tf.Session() as sess:
    y_val, z_val = sess.run([y, z])
    print(y_val)  # 10
    print(z_val)  # 15

10
15

Linear Regression¶

Using the Normal Equation¶

In [19]:

import numpy as np
from sklearn.datasets import fetch_california_housing

reset_graph()

housing = fetch_california_housing()
m, n = housing.data.shape
housing_data_plus_bias = np.c_[np.ones((m, 1)), housing.data]

X = tf.constant(housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
XT = tf.transpose(X)
theta = tf.matmul(tf.matmul(tf.matrix_inverse(tf.matmul(XT, X)), XT), y)

with tf.Session() as sess:
    theta_value = theta.eval()

In [20]:

theta_value

Out[20]:

array([[-3.7185181e+01],
       [ 4.3633747e-01],
       [ 9.3952334e-03],
       [-1.0711310e-01],
       [ 6.4479220e-01],
       [-4.0338000e-06],
       [-3.7813708e-03],
       [-4.2348403e-01],
       [-4.3721911e-01]], dtype=float32)

Compare with pure NumPy

In [21]:

X = housing_data_plus_bias
y = housing.target.reshape(-1, 1)
theta_numpy = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)

print(theta_numpy)

[[-3.69419202e+01]
 [ 4.36693293e-01]
 [ 9.43577803e-03]
 [-1.07322041e-01]
 [ 6.45065694e-01]
 [-3.97638942e-06]
 [-3.78654265e-03]
 [-4.21314378e-01]
 [-4.34513755e-01]]

Compare with Scikit-Learn

In [22]:

from sklearn.linear_model import LinearRegression
lin_reg = LinearRegression()
lin_reg.fit(housing.data, housing.target.reshape(-1, 1))

print(np.r_[lin_reg.intercept_.reshape(-1, 1), lin_reg.coef_.T])

[[-3.69419202e+01]
 [ 4.36693293e-01]
 [ 9.43577803e-03]
 [-1.07322041e-01]
 [ 6.45065694e-01]
 [-3.97638942e-06]
 [-3.78654265e-03]
 [-4.21314378e-01]
 [-4.34513755e-01]]

Using Batch Gradient Descent¶

Gradient Descent requires scaling the feature vectors first. We could do this using TF, but let's just use Scikit-Learn for now.

In [23]:

from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaled_housing_data = scaler.fit_transform(housing.data)
scaled_housing_data_plus_bias = np.c_[np.ones((m, 1)), scaled_housing_data]

In [24]:

print(scaled_housing_data_plus_bias.mean(axis=0))
print(scaled_housing_data_plus_bias.mean(axis=1))
print(scaled_housing_data_plus_bias.mean())
print(scaled_housing_data_plus_bias.shape)

[ 1.00000000e+00  6.60969987e-17  5.50808322e-18  6.60969987e-17
 -1.06030602e-16 -1.10161664e-17  3.44255201e-18 -1.07958431e-15
 -8.52651283e-15]
[ 0.38915536  0.36424355  0.5116157  ... -0.06612179 -0.06360587
  0.01359031]
0.11111111111111005
(20640, 9)

Manually computing the gradients¶

In [25]:

reset_graph()

n_epochs = 1000
learning_rate = 0.01

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
gradients = 2/m * tf.matmul(tf.transpose(X), error)
training_op = tf.assign(theta, theta - learning_rate * gradients)

init = tf.global_variables_initializer()

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

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    
    best_theta = theta.eval()

Epoch 0 MSE = 9.161542
Epoch 100 MSE = 0.7145004
Epoch 200 MSE = 0.56670487
Epoch 300 MSE = 0.5555718
Epoch 400 MSE = 0.5488112
Epoch 500 MSE = 0.5436363
Epoch 600 MSE = 0.5396291
Epoch 700 MSE = 0.5365092
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.5321473

In [26]:

best_theta

Out[26]:

array([[ 2.0685523 ],
       [ 0.8874027 ],
       [ 0.14401656],
       [-0.34770882],
       [ 0.36178368],
       [ 0.00393811],
       [-0.04269556],
       [-0.6614529 ],
       [-0.6375279 ]], dtype=float32)

Using autodiff¶

Same as above except for the gradients = ... line:

In [27]:

reset_graph()

n_epochs = 1000
learning_rate = 0.01

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")

In [28]:

gradients = tf.gradients(mse, [theta])[0]

In [29]:

training_op = tf.assign(theta, theta - learning_rate * gradients)

init = tf.global_variables_initializer()

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

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    
    best_theta = theta.eval()

print("Best theta:")
print(best_theta)

Epoch 0 MSE = 9.161542
Epoch 100 MSE = 0.71450037
Epoch 200 MSE = 0.56670487
Epoch 300 MSE = 0.5555718
Epoch 400 MSE = 0.54881126
Epoch 500 MSE = 0.5436363
Epoch 600 MSE = 0.53962916
Epoch 700 MSE = 0.5365092
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.5321473
Best theta:
[[ 2.0685523 ]
 [ 0.8874027 ]
 [ 0.14401656]
 [-0.3477088 ]
 [ 0.36178365]
 [ 0.00393811]
 [-0.04269556]
 [-0.66145283]
 [-0.6375278 ]]

How could you find the partial derivatives of the following function with regards to a and b?

In [30]:

def my_func(a, b):
    z = 0
    for i in range(100):
        z = a * np.cos(z + i) + z * np.sin(b - i)
    return z

In [31]:

my_func(0.2, 0.3)

Out[31]:

-0.21253923284754914

In [32]:

reset_graph()

a = tf.Variable(0.2, name="a")
b = tf.Variable(0.3, name="b")
z = tf.constant(0.0, name="z0")
for i in range(100):
    z = a * tf.cos(z + i) + z * tf.sin(b - i)

grads = tf.gradients(z, [a, b])
init = tf.global_variables_initializer()

Let's compute the function at $a=0.2$ and $b=0.3$, and the partial derivatives at that point with regards to $a$ and with regards to $b$:

In [33]:

with tf.Session() as sess:
    init.run()
    print(z.eval())
    print(sess.run(grads))

-0.21253741
[-1.1388495, 0.19671397]

Using a `GradientDescentOptimizer`¶

In [34]:

reset_graph()

n_epochs = 1000
learning_rate = 0.01

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")

In [35]:

optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)

In [36]:

init = tf.global_variables_initializer()

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

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    
    best_theta = theta.eval()

print("Best theta:")
print(best_theta)

Epoch 0 MSE = 9.161542
Epoch 100 MSE = 0.7145004
Epoch 200 MSE = 0.56670487
Epoch 300 MSE = 0.5555718
Epoch 400 MSE = 0.54881126
Epoch 500 MSE = 0.5436363
Epoch 600 MSE = 0.53962916
Epoch 700 MSE = 0.5365092
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.5321473
Best theta:
[[ 2.0685523 ]
 [ 0.8874027 ]
 [ 0.14401656]
 [-0.3477088 ]
 [ 0.36178365]
 [ 0.00393811]
 [-0.04269556]
 [-0.66145283]
 [-0.6375278 ]]

Using a momentum optimizer¶

In [37]:

reset_graph()

n_epochs = 1000
learning_rate = 0.01

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")

In [38]:

optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,
                                       momentum=0.9)

In [39]:

training_op = optimizer.minimize(mse)

init = tf.global_variables_initializer()

In [40]:

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

    for epoch in range(n_epochs):
        sess.run(training_op)
    
    best_theta = theta.eval()

print("Best theta:")
print(best_theta)

Best theta:
[[ 2.068558  ]
 [ 0.82962847]
 [ 0.11875335]
 [-0.26554456]
 [ 0.3057109 ]
 [-0.00450249]
 [-0.03932662]
 [-0.8998645 ]
 [-0.8705207 ]]

Feeding data to the training algorithm¶

Placeholder nodes¶

In [41]:

reset_graph()

A = tf.placeholder(tf.float32, shape=(None, 3))
B = A + 5
with tf.Session() as sess:
    B_val_1 = B.eval(feed_dict={A: [[1, 2, 3]]})
    B_val_2 = B.eval(feed_dict={A: [[4, 5, 6], [7, 8, 9]]})

print(B_val_1)

[[6. 7. 8.]]

In [42]:

print(B_val_2)

[[ 9. 10. 11.]
 [12. 13. 14.]]

Mini-batch Gradient Descent¶

In [43]:

n_epochs = 1000
learning_rate = 0.01

In [44]:

reset_graph()

X = tf.placeholder(tf.float32, shape=(None, n + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")

In [45]:

theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)

init = tf.global_variables_initializer()

In [46]:

n_epochs = 10

In [47]:

batch_size = 100
n_batches = int(np.ceil(m / batch_size))

In [48]:

def fetch_batch(epoch, batch_index, batch_size):
    np.random.seed(epoch * n_batches + batch_index)  # not shown in the book
    indices = np.random.randint(m, size=batch_size)  # not shown
    X_batch = scaled_housing_data_plus_bias[indices] # not shown
    y_batch = housing.target.reshape(-1, 1)[indices] # not shown
    return X_batch, y_batch

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

    for epoch in range(n_epochs):
        for batch_index in range(n_batches):
            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})

    best_theta = theta.eval()

In [49]:

best_theta

Out[49]:

array([[ 2.0703337 ],
       [ 0.8637145 ],
       [ 0.12255152],
       [-0.31211877],
       [ 0.38510376],
       [ 0.00434168],
       [-0.0123295 ],
       [-0.83376896],
       [-0.8030471 ]], dtype=float32)

Saving and restoring a model¶

In [50]:

reset_graph()

n_epochs = 1000                                                                       # not shown in the book
learning_rate = 0.01                                                                  # not shown

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")            # not shown
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")            # not shown
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")                                      # not shown
error = y_pred - y                                                                    # not shown
mse = tf.reduce_mean(tf.square(error), name="mse")                                    # not shown
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)            # not shown
training_op = optimizer.minimize(mse)                                                 # not shown

init = tf.global_variables_initializer()
saver = tf.train.Saver()

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

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())                                # not shown
            save_path = saver.save(sess, "/tmp/my_model.ckpt")
        sess.run(training_op)
    
    best_theta = theta.eval()
    save_path = saver.save(sess, "/tmp/my_model_final.ckpt")

Epoch 0 MSE = 9.161542
Epoch 100 MSE = 0.7145004
Epoch 200 MSE = 0.56670487
Epoch 300 MSE = 0.5555718
Epoch 400 MSE = 0.54881126
Epoch 500 MSE = 0.5436363
Epoch 600 MSE = 0.53962916
Epoch 700 MSE = 0.5365092
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.5321473

In [51]:

best_theta

Out[51]:

array([[ 2.0685523 ],
       [ 0.8874027 ],
       [ 0.14401656],
       [-0.3477088 ],
       [ 0.36178365],
       [ 0.00393811],
       [-0.04269556],
       [-0.66145283],
       [-0.6375278 ]], dtype=float32)

In [52]:

with tf.Session() as sess:
    saver.restore(sess, "/tmp/my_model_final.ckpt")
    best_theta_restored = theta.eval() # not shown in the book

INFO:tensorflow:Restoring parameters from /tmp/my_model_final.ckpt

In [53]:

np.allclose(best_theta, best_theta_restored)

Out[53]:

True

If you want to have a saver that loads and restores theta with a different name, such as "weights":

In [54]:

saver = tf.train.Saver({"weights": theta})

By default the saver also saves the graph structure itself in a second file with the extension .meta. You can use the function tf.train.import_meta_graph() to restore the graph structure. This function loads the graph into the default graph and returns a Saver that can then be used to restore the graph state (i.e., the variable values):

In [55]:

reset_graph()
# notice that we start with an empty graph.

saver = tf.train.import_meta_graph("/tmp/my_model_final.ckpt.meta")  # this loads the graph structure
theta = tf.get_default_graph().get_tensor_by_name("theta:0") # not shown in the book

with tf.Session() as sess:
    saver.restore(sess, "/tmp/my_model_final.ckpt")  # this restores the graph's state
    best_theta_restored = theta.eval() # not shown in the book

INFO:tensorflow:Restoring parameters from /tmp/my_model_final.ckpt

In [56]:

np.allclose(best_theta, best_theta_restored)

Out[56]:

True

This means that you can import a pretrained model without having to have the corresponding Python code to build the graph. This is very handy when you keep tweaking and saving your model: you can load a previously saved model without having to search for the version of the code that built it.

Visualizing the graph¶

inside Jupyter¶

To visualize the graph within Jupyter, we will use a TensorBoard server available online at https://tensorboard.appspot.com/ (so this will not work if you do not have Internet access). As far as I can tell, this code was originally written by Alex Mordvintsev in his DeepDream tutorial. Alternatively, you could use a tool like tfgraphviz.

In [57]:

from tensorflow_graph_in_jupyter import show_graph

In [58]:

show_graph(tf.get_default_graph())

Using TensorBoard¶

In [59]:

reset_graph()

from datetime import datetime

now = datetime.utcnow().strftime("%Y%m%d%H%M%S")
root_logdir = "tf_logs"
logdir = "{}/run-{}/".format(root_logdir, now)

In [60]:

n_epochs = 1000
learning_rate = 0.01

X = tf.placeholder(tf.float32, shape=(None, n + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)

init = tf.global_variables_initializer()

In [61]:

mse_summary = tf.summary.scalar('MSE', mse)
file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())

In [62]:

n_epochs = 10
batch_size = 100
n_batches = int(np.ceil(m / batch_size))

In [63]:

with tf.Session() as sess:                                                        # not shown in the book
    sess.run(init)                                                                # not shown

    for epoch in range(n_epochs):                                                 # not shown
        for batch_index in range(n_batches):
            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)
            if batch_index % 10 == 0:
                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})
                step = epoch * n_batches + batch_index
                file_writer.add_summary(summary_str, step)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})

    best_theta = theta.eval()                                                     # not shown

In [64]:

file_writer.close()

In [65]:

best_theta

Out[65]:

array([[ 2.07033372],
       [ 0.86371452],
       [ 0.12255151],
       [-0.31211874],
       [ 0.38510373],
       [ 0.00434168],
       [-0.01232954],
       [-0.83376896],
       [-0.80304712]], dtype=float32)

Name scopes¶

In [66]:

reset_graph()

now = datetime.utcnow().strftime("%Y%m%d%H%M%S")
root_logdir = "tf_logs"
logdir = "{}/run-{}/".format(root_logdir, now)

n_epochs = 1000
learning_rate = 0.01

X = tf.placeholder(tf.float32, shape=(None, n + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")

In [67]:

with tf.name_scope("loss") as scope:
    error = y_pred - y
    mse = tf.reduce_mean(tf.square(error), name="mse")

In [68]:

optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)

init = tf.global_variables_initializer()

mse_summary = tf.summary.scalar('MSE', mse)
file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())

In [69]:

n_epochs = 10
batch_size = 100
n_batches = int(np.ceil(m / batch_size))

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

    for epoch in range(n_epochs):
        for batch_index in range(n_batches):
            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)
            if batch_index % 10 == 0:
                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})
                step = epoch * n_batches + batch_index
                file_writer.add_summary(summary_str, step)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})

    best_theta = theta.eval()

file_writer.flush()
file_writer.close()
print("Best theta:")
print(best_theta)

Best theta:
[[ 2.07033372]
 [ 0.86371452]
 [ 0.12255151]
 [-0.31211874]
 [ 0.38510373]
 [ 0.00434168]
 [-0.01232954]
 [-0.83376896]
 [-0.80304712]]

In [70]:

print(error.op.name)

loss/sub

In [71]:

print(mse.op.name)

loss/mse

In [72]:

reset_graph()

a1 = tf.Variable(0, name="a")      # name == "a"
a2 = tf.Variable(0, name="a")      # name == "a_1"

with tf.name_scope("param"):       # name == "param"
    a3 = tf.Variable(0, name="a")  # name == "param/a"

with tf.name_scope("param"):       # name == "param_1"
    a4 = tf.Variable(0, name="a")  # name == "param_1/a"

for node in (a1, a2, a3, a4):
    print(node.op.name)

a
a_1
param/a
param_1/a

Modularity¶

An ugly flat code:

In [73]:

reset_graph()

n_features = 3
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")

w1 = tf.Variable(tf.random_normal((n_features, 1)), name="weights1")
w2 = tf.Variable(tf.random_normal((n_features, 1)), name="weights2")
b1 = tf.Variable(0.0, name="bias1")
b2 = tf.Variable(0.0, name="bias2")

z1 = tf.add(tf.matmul(X, w1), b1, name="z1")
z2 = tf.add(tf.matmul(X, w2), b2, name="z2")

relu1 = tf.maximum(z1, 0., name="relu1")
relu2 = tf.maximum(z1, 0., name="relu2")  # Oops, cut&paste error! Did you spot it?

output = tf.add(relu1, relu2, name="output")

Much better, using a function to build the ReLUs:

In [74]:

reset_graph()

def relu(X):
    w_shape = (int(X.get_shape()[1]), 1)
    w = tf.Variable(tf.random_normal(w_shape), name="weights")
    b = tf.Variable(0.0, name="bias")
    z = tf.add(tf.matmul(X, w), b, name="z")
    return tf.maximum(z, 0., name="relu")

n_features = 3
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X) for i in range(5)]
output = tf.add_n(relus, name="output")

In [75]:

file_writer = tf.summary.FileWriter("logs/relu1", tf.get_default_graph())

Even better using name scopes:

In [76]:

reset_graph()

def relu(X):
    with tf.name_scope("relu"):
        w_shape = (int(X.get_shape()[1]), 1)                          # not shown in the book
        w = tf.Variable(tf.random_normal(w_shape), name="weights")    # not shown
        b = tf.Variable(0.0, name="bias")                             # not shown
        z = tf.add(tf.matmul(X, w), b, name="z")                      # not shown
        return tf.maximum(z, 0., name="max")                          # not shown

In [77]:

n_features = 3
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X) for i in range(5)]
output = tf.add_n(relus, name="output")

file_writer = tf.summary.FileWriter("logs/relu2", tf.get_default_graph())
file_writer.close()

Sharing a threshold variable the classic way, by defining it outside of the relu() function then passing it as a parameter:

In [78]:

reset_graph()

def relu(X, threshold):
    with tf.name_scope("relu"):
        w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book
        w = tf.Variable(tf.random_normal(w_shape), name="weights")  # not shown
        b = tf.Variable(0.0, name="bias")                           # not shown
        z = tf.add(tf.matmul(X, w), b, name="z")                    # not shown
        return tf.maximum(z, threshold, name="max")

threshold = tf.Variable(0.0, name="threshold")
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X, threshold) for i in range(5)]
output = tf.add_n(relus, name="output")

In [79]:

reset_graph()

def relu(X):
    with tf.name_scope("relu"):
        if not hasattr(relu, "threshold"):
            relu.threshold = tf.Variable(0.0, name="threshold")
        w_shape = int(X.get_shape()[1]), 1                          # not shown in the book
        w = tf.Variable(tf.random_normal(w_shape), name="weights")  # not shown
        b = tf.Variable(0.0, name="bias")                           # not shown
        z = tf.add(tf.matmul(X, w), b, name="z")                    # not shown
        return tf.maximum(z, relu.threshold, name="max")

In [80]:

X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X) for i in range(5)]
output = tf.add_n(relus, name="output")

In [81]:

reset_graph()

with tf.variable_scope("relu"):
    threshold = tf.get_variable("threshold", shape=(),
                                initializer=tf.constant_initializer(0.0))

In [82]:

with tf.variable_scope("relu", reuse=True):
    threshold = tf.get_variable("threshold")

In [83]:

with tf.variable_scope("relu") as scope:
    scope.reuse_variables()
    threshold = tf.get_variable("threshold")

In [84]:

reset_graph()

def relu(X):
    with tf.variable_scope("relu", reuse=True):
        threshold = tf.get_variable("threshold")
        w_shape = int(X.get_shape()[1]), 1                          # not shown
        w = tf.Variable(tf.random_normal(w_shape), name="weights")  # not shown
        b = tf.Variable(0.0, name="bias")                           # not shown
        z = tf.add(tf.matmul(X, w), b, name="z")                    # not shown
        return tf.maximum(z, threshold, name="max")

X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
with tf.variable_scope("relu"):
    threshold = tf.get_variable("threshold", shape=(),
                                initializer=tf.constant_initializer(0.0))
relus = [relu(X) for relu_index in range(5)]
output = tf.add_n(relus, name="output")

In [85]:

file_writer = tf.summary.FileWriter("logs/relu6", tf.get_default_graph())
file_writer.close()

In [86]:

reset_graph()

def relu(X):
    with tf.variable_scope("relu"):
        threshold = tf.get_variable("threshold", shape=(), initializer=tf.constant_initializer(0.0))
        w_shape = (int(X.get_shape()[1]), 1)
        w = tf.Variable(tf.random_normal(w_shape), name="weights")
        b = tf.Variable(0.0, name="bias")
        z = tf.add(tf.matmul(X, w), b, name="z")
        return tf.maximum(z, threshold, name="max")

X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
with tf.variable_scope("", default_name="") as scope:
    first_relu = relu(X)     # create the shared variable
    scope.reuse_variables()  # then reuse it
    relus = [first_relu] + [relu(X) for i in range(4)]
output = tf.add_n(relus, name="output")

file_writer = tf.summary.FileWriter("logs/relu8", tf.get_default_graph())
file_writer.close()

In [87]:

reset_graph()

def relu(X):
    threshold = tf.get_variable("threshold", shape=(),
                                initializer=tf.constant_initializer(0.0))
    w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book
    w = tf.Variable(tf.random_normal(w_shape), name="weights")  # not shown
    b = tf.Variable(0.0, name="bias")                           # not shown
    z = tf.add(tf.matmul(X, w), b, name="z")                    # not shown
    return tf.maximum(z, threshold, name="max")

X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = []
for relu_index in range(5):
    with tf.variable_scope("relu", reuse=(relu_index >= 1)) as scope:
        relus.append(relu(X))
output = tf.add_n(relus, name="output")

In [88]:

file_writer = tf.summary.FileWriter("logs/relu9", tf.get_default_graph())
file_writer.close()

Extra material¶

In [89]:

reset_graph()

with tf.variable_scope("my_scope"):
    x0 = tf.get_variable("x", shape=(), initializer=tf.constant_initializer(0.))
    x1 = tf.Variable(0., name="x")
    x2 = tf.Variable(0., name="x")

with tf.variable_scope("my_scope", reuse=True):
    x3 = tf.get_variable("x")
    x4 = tf.Variable(0., name="x")

with tf.variable_scope("", default_name="", reuse=True):
    x5 = tf.get_variable("my_scope/x")

print("x0:", x0.op.name)
print("x1:", x1.op.name)
print("x2:", x2.op.name)
print("x3:", x3.op.name)
print("x4:", x4.op.name)
print("x5:", x5.op.name)
print(x0 is x3 and x3 is x5)

x0: my_scope/x
x1: my_scope/x_1
x2: my_scope/x_2
x3: my_scope/x
x4: my_scope_1/x
x5: my_scope/x
True

The first variable_scope() block first creates the shared variable x0, named my_scope/x. For all operations other than shared variables (including non-shared variables), the variable scope acts like a regular name scope, which is why the two variables x1 and x2 have a name with a prefix my_scope/. Note however that TensorFlow makes their names unique by adding an index: my_scope/x_1 and my_scope/x_2.

The second variable_scope() block reuses the shared variables in scope my_scope, which is why x0 is x3. Once again, for all operations other than shared variables it acts as a named scope, and since it's a separate block from the first one, the name of the scope is made unique by TensorFlow (my_scope_1) and thus the variable x4 is named my_scope_1/x.

The third block shows another way to get a handle on the shared variable my_scope/x by creating a variable_scope() at the root scope (whose name is an empty string), then calling get_variable() with the full name of the shared variable (i.e. "my_scope/x").

Strings¶

In [90]:

reset_graph()

text = np.array("Do you want some café?".split())
text_tensor = tf.constant(text)

with tf.Session() as sess:
    print(text_tensor.eval())

[b'Do' b'you' b'want' b'some' b'caf\xc3\xa9?']

Autodiff¶

Note: the autodiff content was moved to the extra_autodiff.ipynb notebook.

Exercise solutions¶

1. to 11.¶

See appendix A.

12. Logistic Regression with Mini-Batch Gradient Descent using TensorFlow¶

First, let's create the moons dataset using Scikit-Learn's make_moons() function:

In [91]:

from sklearn.datasets import make_moons

m = 1000
X_moons, y_moons = make_moons(m, noise=0.1, random_state=42)

Let's take a peek at the dataset:

In [92]:

plt.plot(X_moons[y_moons == 1, 0], X_moons[y_moons == 1, 1], 'go', label="Positive")
plt.plot(X_moons[y_moons == 0, 0], X_moons[y_moons == 0, 1], 'r^', label="Negative")
plt.legend()
plt.show()

We must not forget to add an extra bias feature ($x_0 = 1$) to every instance. For this, we just need to add a column full of 1s on the left of the input matrix $\mathbf{X}$:

In [93]:

X_moons_with_bias = np.c_[np.ones((m, 1)), X_moons]

Let's check:

In [94]:

X_moons_with_bias[:5]

Out[94]:

array([[ 1.        , -0.05146968,  0.44419863],
       [ 1.        ,  1.03201691, -0.41974116],
       [ 1.        ,  0.86789186, -0.25482711],
       [ 1.        ,  0.288851  , -0.44866862],
       [ 1.        , -0.83343911,  0.53505665]])

Looks good. Now let's reshape y_train to make it a column vector (i.e. a 2D array with a single column):

In [95]:

y_moons_column_vector = y_moons.reshape(-1, 1)

Now let's split the data into a training set and a test set:

In [96]:

test_ratio = 0.2
test_size = int(m * test_ratio)
X_train = X_moons_with_bias[:-test_size]
X_test = X_moons_with_bias[-test_size:]
y_train = y_moons_column_vector[:-test_size]
y_test = y_moons_column_vector[-test_size:]

Ok, now let's create a small function to generate training batches. In this implementation we will just pick random instances from the training set for each batch. This means that a single batch may contain the same instance multiple times, and also a single epoch may not cover all the training instances (in fact it will generally cover only about two thirds of the instances). However, in practice this is not an issue and it simplifies the code:

In [97]:

def random_batch(X_train, y_train, batch_size):
    rnd_indices = np.random.randint(0, len(X_train), batch_size)
    X_batch = X_train[rnd_indices]
    y_batch = y_train[rnd_indices]
    return X_batch, y_batch

Let's look at a small batch:

In [98]:

X_batch, y_batch = random_batch(X_train, y_train, 5)
X_batch

Out[98]:

array([[ 1.        ,  1.93189866,  0.13158788],
       [ 1.        ,  1.07172763,  0.13482039],
       [ 1.        , -1.01148674, -0.04686381],
       [ 1.        ,  0.02201868,  0.19079139],
       [ 1.        , -0.98941204,  0.02473116]])

In [99]:

y_batch

Out[99]:

array([[1],
       [0],
       [0],
       [1],
       [0]])

Great! Now that the data is ready to be fed to the model, we need to build that model. Let's start with a simple implementation, then we will add all the bells and whistles.

First let's reset the default graph.

In [100]:

reset_graph()

The moons dataset has two input features, since each instance is a point on a plane (i.e., 2-Dimensional):

In [101]:

n_inputs = 2

Now let's build the Logistic Regression model. As we saw in chapter 4, this model first computes a weighted sum of the inputs (just like the Linear Regression model), and then it applies the sigmoid function to the result, which gives us the estimated probability for the positive class:

$\hat{p} = h_\boldsymbol{\theta}(\mathbf{x}) = \sigma(\boldsymbol{\theta}^T \mathbf{x})$

Recall that $\boldsymbol{\theta}$ is the parameter vector, containing the bias term $\theta_0$ and the weights $\theta_1, \theta_2, \dots, \theta_n$. The input vector $\mathbf{x}$ contains a constant term $x_0 = 1$, as well as all the input features $x_1, x_2, \dots, x_n$.

Since we want to be able to make predictions for multiple instances at a time, we will use an input matrix $\mathbf{X}$ rather than a single input vector. The $i^{th}$ row will contain the transpose of the $i^{th}$ input vector $(\mathbf{x}^{(i)})^T$. It is then possible to estimate the probability that each instance belongs to the positive class using the following equation:

$ \hat{\mathbf{p}} = \sigma(\mathbf{X} \boldsymbol{\theta})$

That's all we need to build the model:

In [102]:

X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")
theta = tf.Variable(tf.random_uniform([n_inputs + 1, 1], -1.0, 1.0, seed=42), name="theta")
logits = tf.matmul(X, theta, name="logits")
y_proba = 1 / (1 + tf.exp(-logits))

In fact, TensorFlow has a nice function tf.sigmoid() that we can use to simplify the last line of the previous code:

In [103]:

y_proba = tf.sigmoid(logits)

As we saw in chapter 4, the log loss is a good cost function to use for Logistic Regression:

$J(\boldsymbol{\theta}) = -\dfrac{1}{m} \sum\limits_{i=1}^{m}{\left[ y^{(i)} \log\left(\hat{p}^{(i)}\right) + (1 - y^{(i)}) \log\left(1 - \hat{p}^{(i)}\right)\right]}$

One option is to implement it ourselves:

In [104]:

epsilon = 1e-7  # to avoid an overflow when computing the log
loss = -tf.reduce_mean(y * tf.log(y_proba + epsilon) + (1 - y) * tf.log(1 - y_proba + epsilon))

But we might as well use TensorFlow's tf.losses.log_loss() function:

In [105]:

loss = tf.losses.log_loss(y, y_proba)  # uses epsilon = 1e-7 by default

The rest is pretty standard: let's create the optimizer and tell it to minimize the cost function:

In [106]:

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

All we need now (in this minimal version) is the variable initializer:

In [107]:

init = tf.global_variables_initializer()

And we are ready to train the model and use it for predictions!

There's really nothing special about this code, it's virtually the same as the one we used earlier for Linear Regression:

In [108]:

n_epochs = 1000
batch_size = 50
n_batches = int(np.ceil(m / batch_size))

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

    for epoch in range(n_epochs):
        for batch_index in range(n_batches):
            X_batch, y_batch = random_batch(X_train, y_train, batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
        loss_val = loss.eval({X: X_test, y: y_test})
        if epoch % 100 == 0:
            print("Epoch:", epoch, "\tLoss:", loss_val)

    y_proba_val = y_proba.eval(feed_dict={X: X_test, y: y_test})

Epoch: 0 	Loss: 0.792602
Epoch: 100 	Loss: 0.343463
Epoch: 200 	Loss: 0.30754
Epoch: 300 	Loss: 0.292889
Epoch: 400 	Loss: 0.285336
Epoch: 500 	Loss: 0.280478
Epoch: 600 	Loss: 0.278083
Epoch: 700 	Loss: 0.276154
Epoch: 800 	Loss: 0.27552
Epoch: 900 	Loss: 0.274912

Note: we don't use the epoch number when generating batches, so we could just have a single for loop rather than 2 nested for loops, but it's convenient to think of training time in terms of number of epochs (i.e., roughly the number of times the algorithm went through the training set).

For each instance in the test set, y_proba_val contains the estimated probability that it belongs to the positive class, according to the model. For example, here are the first 5 estimated probabilities:

In [109]:

y_proba_val[:5]

Out[109]:

array([[ 0.54895616],
       [ 0.70724374],
       [ 0.51900256],
       [ 0.9911136 ],
       [ 0.50859052]], dtype=float32)

To classify each instance, we can go for maximum likelihood: classify as positive any instance whose estimated probability is greater or equal to 0.5:

In [110]:

y_pred = (y_proba_val >= 0.5)
y_pred[:5]

Out[110]:

array([[ True],
       [ True],
       [ True],
       [ True],
       [ True]], dtype=bool)

Depending on the use case, you may want to choose a different threshold than 0.5: make it higher if you want high precision (but lower recall), and make it lower if you want high recall (but lower precision). See chapter 3 for more details.

Let's compute the model's precision and recall:

In [111]:

from sklearn.metrics import precision_score, recall_score

precision_score(y_test, y_pred)

Out[111]:

0.86274509803921573

In [112]:

recall_score(y_test, y_pred)

Out[112]:

0.88888888888888884

Let's plot these predictions to see what they look like:

In [113]:

y_pred_idx = y_pred.reshape(-1) # a 1D array rather than a column vector
plt.plot(X_test[y_pred_idx, 1], X_test[y_pred_idx, 2], 'go', label="Positive")
plt.plot(X_test[~y_pred_idx, 1], X_test[~y_pred_idx, 2], 'r^', label="Negative")
plt.legend()
plt.show()

Well, that looks pretty bad, doesn't it? But let's not forget that the Logistic Regression model has a linear decision boundary, so this is actually close to the best we can do with this model (unless we add more features, as we will show in a second).

Now let's start over, but this time we will add all the bells and whistles, as listed in the exercise:

Define the graph within a logistic_regression() function that can be reused easily.
Save checkpoints using a Saver at regular intervals during training, and save the final model at the end of training.
Restore the last checkpoint upon startup if training was interrupted.
Define the graph using nice scopes so the graph looks good in TensorBoard.
Add summaries to visualize the learning curves in TensorBoard.
Try tweaking some hyperparameters such as the learning rate or the mini-batch size and look at the shape of the learning curve.

Before we start, we will add 4 more features to the inputs: ${x_1}^2$, ${x_2}^2$, ${x_1}^3$ and ${x_2}^3$. This was not part of the exercise, but it will demonstrate how adding features can improve the model. We will do this manually, but you could also add them using sklearn.preprocessing.PolynomialFeatures.

In [114]:

X_train_enhanced = np.c_[X_train,
                         np.square(X_train[:, 1]),
                         np.square(X_train[:, 2]),
                         X_train[:, 1] ** 3,
                         X_train[:, 2] ** 3]
X_test_enhanced = np.c_[X_test,
                        np.square(X_test[:, 1]),
                        np.square(X_test[:, 2]),
                        X_test[:, 1] ** 3,
                        X_test[:, 2] ** 3]

This is what the "enhanced" training set looks like:

In [115]:

X_train_enhanced[:5]

Out[115]:

array([[  1.00000000e+00,  -5.14696757e-02,   4.44198631e-01,
          2.64912752e-03,   1.97312424e-01,  -1.36349734e-04,
          8.76459084e-02],
       [  1.00000000e+00,   1.03201691e+00,  -4.19741157e-01,
          1.06505890e+00,   1.76182639e-01,   1.09915879e+00,
         -7.39511049e-02],
       [  1.00000000e+00,   8.67891864e-01,  -2.54827114e-01,
          7.53236288e-01,   6.49368582e-02,   6.53727646e-01,
         -1.65476722e-02],
       [  1.00000000e+00,   2.88850997e-01,  -4.48668621e-01,
          8.34348982e-02,   2.01303531e-01,   2.41002535e-02,
         -9.03185778e-02],
       [  1.00000000e+00,  -8.33439108e-01,   5.35056649e-01,
          6.94620746e-01,   2.86285618e-01,  -5.78924095e-01,
          1.53179024e-01]])

Ok, next let's reset the default graph:

In [116]:

reset_graph()

Now let's define the logistic_regression() function to create the graph. We will leave out the definition of the inputs X and the targets y. We could include them here, but leaving them out will make it easier to use this function in a wide range of use cases (e.g. perhaps we will want to add some preprocessing steps for the inputs before we feed them to the Logistic Regression model).

In [117]:

def logistic_regression(X, y, initializer=None, seed=42, learning_rate=0.01):
    n_inputs_including_bias = int(X.get_shape()[1])
    with tf.name_scope("logistic_regression"):
        with tf.name_scope("model"):
            if initializer is None:
                initializer = tf.random_uniform([n_inputs_including_bias, 1], -1.0, 1.0, seed=seed)
            theta = tf.Variable(initializer, name="theta")
            logits = tf.matmul(X, theta, name="logits")
            y_proba = tf.sigmoid(logits)
        with tf.name_scope("train"):
            loss = tf.losses.log_loss(y, y_proba, scope="loss")
            optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
            training_op = optimizer.minimize(loss)
            loss_summary = tf.summary.scalar('log_loss', loss)
        with tf.name_scope("init"):
            init = tf.global_variables_initializer()
        with tf.name_scope("save"):
            saver = tf.train.Saver()
    return y_proba, loss, training_op, loss_summary, init, saver

Let's create a little function to get the name of the log directory to save the summaries for Tensorboard:

In [118]:

from datetime import datetime

def log_dir(prefix=""):
    now = datetime.utcnow().strftime("%Y%m%d%H%M%S")
    root_logdir = "tf_logs"
    if prefix:
        prefix += "-"
    name = prefix + "run-" + now
    return "{}/{}/".format(root_logdir, name)

Next, let's create the graph, using the logistic_regression() function. We will also create the FileWriter to save the summaries to the log directory for Tensorboard:

In [119]:

n_inputs = 2 + 4
logdir = log_dir("logreg")

X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")

y_proba, loss, training_op, loss_summary, init, saver = logistic_regression(X, y)

file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())

At last we can train the model! We will start by checking whether a previous training session was interrupted, and if so we will load the checkpoint and continue training from the epoch number we saved. In this example we just save the epoch number to a separate file, but in chapter 11 we will see how to store the training step directly as part of the model, using a non-trainable variable called global_step that we pass to the optimizer's minimize() method.

You can try interrupting training to verify that it does indeed restore the last checkpoint when you start it again.

In [120]:

n_epochs = 10001
batch_size = 50
n_batches = int(np.ceil(m / batch_size))

checkpoint_path = "/tmp/my_logreg_model.ckpt"
checkpoint_epoch_path = checkpoint_path + ".epoch"
final_model_path = "./my_logreg_model"

with tf.Session() as sess:
    if os.path.isfile(checkpoint_epoch_path):
        # if the checkpoint file exists, restore the model and load the epoch number
        with open(checkpoint_epoch_path, "rb") as f:
            start_epoch = int(f.read())
        print("Training was interrupted. Continuing at epoch", start_epoch)
        saver.restore(sess, checkpoint_path)
    else:
        start_epoch = 0
        sess.run(init)

    for epoch in range(start_epoch, n_epochs):
        for batch_index in range(n_batches):
            X_batch, y_batch = random_batch(X_train_enhanced, y_train, batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
        loss_val, summary_str = sess.run([loss, loss_summary], feed_dict={X: X_test_enhanced, y: y_test})
        file_writer.add_summary(summary_str, epoch)
        if epoch % 500 == 0:
            print("Epoch:", epoch, "\tLoss:", loss_val)
            saver.save(sess, checkpoint_path)
            with open(checkpoint_epoch_path, "wb") as f:
                f.write(b"%d" % (epoch + 1))

    saver.save(sess, final_model_path)
    y_proba_val = y_proba.eval(feed_dict={X: X_test_enhanced, y: y_test})
    os.remove(checkpoint_epoch_path)

Epoch: 0 	Loss: 0.629985
Epoch: 500 	Loss: 0.161224
Epoch: 1000 	Loss: 0.119032
Epoch: 1500 	Loss: 0.0973292
Epoch: 2000 	Loss: 0.0836979
Epoch: 2500 	Loss: 0.0743758
Epoch: 3000 	Loss: 0.0675021
Epoch: 3500 	Loss: 0.0622069
Epoch: 4000 	Loss: 0.0580268
Epoch: 4500 	Loss: 0.054563
Epoch: 5000 	Loss: 0.0517083
Epoch: 5500 	Loss: 0.0492377
Epoch: 6000 	Loss: 0.0471673
Epoch: 6500 	Loss: 0.0453766
Epoch: 7000 	Loss: 0.0438187
Epoch: 7500 	Loss: 0.0423742
Epoch: 8000 	Loss: 0.0410892
Epoch: 8500 	Loss: 0.0399709
Epoch: 9000 	Loss: 0.0389202
Epoch: 9500 	Loss: 0.0380107
Epoch: 10000 	Loss: 0.0371557

Once again, we can make predictions by just classifying as positive all the instances whose estimated probability is greater or equal to 0.5:

In [121]:

y_pred = (y_proba_val >= 0.5)

In [122]:

precision_score(y_test, y_pred)

Out[122]:

0.97979797979797978

In [123]:

recall_score(y_test, y_pred)

Out[123]:

0.97979797979797978

In [124]:

y_pred_idx = y_pred.reshape(-1) # a 1D array rather than a column vector
plt.plot(X_test[y_pred_idx, 1], X_test[y_pred_idx, 2], 'go', label="Positive")
plt.plot(X_test[~y_pred_idx, 1], X_test[~y_pred_idx, 2], 'r^', label="Negative")
plt.legend()
plt.show()

Now that's much, much better! Apparently the new features really helped a lot.

Try starting the tensorboard server, find the latest run and look at the learning curve (i.e., how the loss evaluated on the test set evolves as a function of the epoch number):

$ tensorboard --logdir=tf_logs

Now you can play around with the hyperparameters (e.g. the batch_size or the learning_rate) and run training again and again, comparing the learning curves. You can even automate this process by implementing grid search or randomized search. Below is a simple implementation of a randomized search on both the batch size and the learning rate. For the sake of simplicity, the checkpoint mechanism was removed.

In [125]:

from scipy.stats import reciprocal

n_search_iterations = 10

for search_iteration in range(n_search_iterations):
    batch_size = np.random.randint(1, 100)
    learning_rate = reciprocal(0.0001, 0.1).rvs(random_state=search_iteration)

    n_inputs = 2 + 4
    logdir = log_dir("logreg")
    
    print("Iteration", search_iteration)
    print("  logdir:", logdir)
    print("  batch size:", batch_size)
    print("  learning_rate:", learning_rate)
    print("  training: ", end="")

    reset_graph()

    X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name="X")
    y = tf.placeholder(tf.float32, shape=(None, 1), name="y")

    y_proba, loss, training_op, loss_summary, init, saver = logistic_regression(
        X, y, learning_rate=learning_rate)

    file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())

    n_epochs = 10001
    n_batches = int(np.ceil(m / batch_size))

    final_model_path = "./my_logreg_model_%d" % search_iteration

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

        for epoch in range(n_epochs):
            for batch_index in range(n_batches):
                X_batch, y_batch = random_batch(X_train_enhanced, y_train, batch_size)
                sess.run(training_op, feed_dict={X: X_batch, y: y_batch})
            loss_val, summary_str = sess.run([loss, loss_summary], feed_dict={X: X_test_enhanced, y: y_test})
            file_writer.add_summary(summary_str, epoch)
            if epoch % 500 == 0:
                print(".", end="")

        saver.save(sess, final_model_path)

        print()
        y_proba_val = y_proba.eval(feed_dict={X: X_test_enhanced, y: y_test})
        y_pred = (y_proba_val >= 0.5)
        
        print("  precision:", precision_score(y_test, y_pred))
        print("  recall:", recall_score(y_test, y_pred))

Iteration 0
  logdir: tf_logs/logreg-run-20170606195328/
  batch size: 19
  learning_rate: 0.00443037524522
  training: .....................
  precision: 0.979797979798
  recall: 0.979797979798
Iteration 1
  logdir: tf_logs/logreg-run-20170606195605/
  batch size: 80
  learning_rate: 0.00178264971514
  training: .....................
  precision: 0.969696969697
  recall: 0.969696969697
Iteration 2
  logdir: tf_logs/logreg-run-20170606195646/
  batch size: 73
  learning_rate: 0.00203228544324
  training: .....................
  precision: 0.969696969697
  recall: 0.969696969697
Iteration 3
  logdir: tf_logs/logreg-run-20170606195730/
  batch size: 6
  learning_rate: 0.00449152382514
  training: .....................
  precision: 0.980198019802
  recall: 1.0
Iteration 4
  logdir: tf_logs/logreg-run-20170606200523/
  batch size: 24
  learning_rate: 0.0796323472178
  training: .....................
  precision: 0.980198019802
  recall: 1.0
Iteration 5
  logdir: tf_logs/logreg-run-20170606200726/
  batch size: 75
  learning_rate: 0.000463425058329
  training: .....................
  precision: 0.912621359223
  recall: 0.949494949495
Iteration 6
  logdir: tf_logs/logreg-run-20170606200810/
  batch size: 86
  learning_rate: 0.0477068184194
  training: .....................
  precision: 0.98
  recall: 0.989898989899
Iteration 7
  logdir: tf_logs/logreg-run-20170606200851/
  batch size: 87
  learning_rate: 0.000169404470952
  training: .....................
  precision: 0.888888888889
  recall: 0.808080808081
Iteration 8
  logdir: tf_logs/logreg-run-20170606200932/
  batch size: 61
  learning_rate: 0.0417146119941
  training: .....................
  precision: 0.980198019802
  recall: 1.0
Iteration 9
  logdir: tf_logs/logreg-run-20170606201026/
  batch size: 92
  learning_rate: 0.000107429229684
  training: .....................
  precision: 0.882352941176
  recall: 0.757575757576

The reciprocal() function from SciPy's stats module returns a random distribution that is commonly used when you have no idea of the optimal scale of a hyperparameter. See the exercise solutions for chapter 2 for more details.

In [ ]: