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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Chapter 9 – Up and running with TensorFlow
This notebook contains all the sample code and solutions to the exercices 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
Step1:  Creating and running a graph
Step2:  Managing graphs
Step3:  Linear Regression
Using the Normal Equation
Step4:  Compare with pure NumPy
Step5:  Compare with Scikit-Learn
Step6:  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.
Step7:  Manually computing the gradients
Step8:  Using autodiff
Same as above except for the gradients = ... line
Step9:  How could you find the partial derivatives of the following function with regards to a and b?
Step10:  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 $b$
Step11:  Using a GradientDescentOptimizer
Step12:  Using a momentum optimizer
Step13:  Feeding data to the training algorithm
Placeholder nodes
Step14:  Mini-batch Gradient Descent
Step15:  Saving and restoring a model
Step16:  If you want to have a saver that loads and restores theta with a different name, such as "weights"
Step17:  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)
Step22:  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
Step23:  Using TensorBoard
Step24:  Name scopes
Step25:  Modularity
An ugly flat code
Step26:  Much better, using a function to build the ReLUs
Step27:  Even better using name scopes
Step28:  Sharing Variables
Sharing a threshold variable the classic way, by defining it outside of the relu() function then passing it as a parameter
Step29:  Extra material
Step30:  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
Step31:  Implementing a Home-Made Computation Graph
Step32:  Computing gradients
Mathematical differentiation
Step33:  Numerical differentiation
Step34:  Symbolic differentiation
Step35:  Automatic differentiation (autodiff) – forward mode
Step36:  $3 + (3 + 4 \epsilon) = 6 + 4\epsilon$
Step37:  $(3 + 4ε)\times(5 + 7ε) = 3 \times 5 + 3 \times 7ε + 4ε \times 5 + 4ε \times 7ε = 15 + 21ε + 20ε + 28ε^2 = 15 + 41ε + 28 \times 0 = 15 + 41ε$
Step38:  Autodiff – Reverse mode
Step39:  Autodiff – reverse mode (using TensorFlow)
Step40:  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
Step41:  Let's take a peek at the dataset
Step42:  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 $\mathbf{X}$
Step43:  Let's check
Step44:  Looks good. Now let's reshape y_train to make it a column vector (i.e. a 2D array with a single column)
Step45:  Now let's split the data into a training set and a test set
Step46:  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
Step47:  Let's look at a small batch
Step48:  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.
Step49:  The moons dataset has two input features, since each instance is a point on a plane (i.e., 2-Dimensional)
Step50:  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
Step51:  In fact, TensorFlow has a nice function tf.sigmoid() that we can use to simplify the last line of the previous code
Step52:  As we saw in chapter 4, the log loss is a good cost function to use for Logistic Regression
Step53:  But we might as well use TensorFlow's tf.losses.log_loss() function
Step54:  The rest is pretty standard
Step55:  All we need now (in this minimal version) is the variable initializer
Step56:  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
Step57:  Note
Step58:  To classify each instance, we can go for maximum likelihood
Step59:  Depending on the use case, you may want to choose a different threshold than 0.5
Step60:  Let's plot these predictions to see what they look like
Step61:  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
Step62:  This is what the "enhanced" training set looks like
Step63:  Ok, next let's reset the default graph
Step64:  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).
Step65:  Let's create a little function to get the name of the log directory to save the summaries for Tensorboard
Step66:  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
Step67:  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.
Step68:  Once again, we can make predictions by just classifying as positive all the instances whose estimated probability is greater or equal to 0.5
Step69:  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)
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Python Code:
# 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)
Explanation: Chapter 9 – Up and running with TensorFlow
This notebook contains all the sample code and solutions to the exercices 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:
End of explanation
import tensorflow as tf
reset_graph()
x = tf.Variable(3, name="x")
y = tf.Variable(4, name="y")
f = x*x*y + y + 2
f
sess = tf.Session()
sess.run(x.initializer)
sess.run(y.initializer)
result = sess.run(f)
print(result)
sess.close()
with tf.Session() as sess:
    x.initializer.run()
    y.initializer.run()
    result = f.eval()
result
init = tf.global_variables_initializer()
with tf.Session() as sess:
    init.run()
    result = f.eval()
result
init = tf.global_variables_initializer()
sess = tf.InteractiveSession()
init.run()
result = f.eval()
print(result)
sess.close()
result
Explanation: Creating and running a graph
End of explanation
reset_graph()
x1 = tf.Variable(1)
x1.graph is tf.get_default_graph()
graph = tf.Graph()
with graph.as_default():
    x2 = tf.Variable(2)
x2.graph is graph
x2.graph is tf.get_default_graph()
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
with tf.Session() as sess:
    y_val, z_val = sess.run([y, z])
    print(y_val)  # 10
    print(z_val)  # 15
Explanation: Managing graphs
End of explanation
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()
theta_value
Explanation: Linear Regression
Using the Normal Equation
End of explanation
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)
Explanation: Compare with pure NumPy
End of explanation
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])
Explanation: Compare with Scikit-Learn
End of explanation
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]
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)
Explanation: 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.
End of explanation
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()
best_theta
Explanation: Manually computing the gradients
End of explanation
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 = tf.gradients(mse, [theta])[0]
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)
Explanation: Using autodiff
Same as above except for the gradients = ... line:
End of explanation
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
my_func(0.2, 0.3)
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()
Explanation: How could you find the partial derivatives of the following function with regards to a and b?
End of explanation
with tf.Session() as sess:
    init.run()
    print(z.eval())
    print(sess.run(grads))
Explanation: 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 $b$:
End of explanation
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")
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)
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)
Explanation: Using a GradientDescentOptimizer
End of explanation
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")
optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,
                                       momentum=0.9)
training_op = optimizer.minimize(mse)
init = tf.global_variables_initializer()
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)
Explanation: Using a momentum optimizer
End of explanation
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)
print(B_val_2)
Explanation: Feeding data to the training algorithm
Placeholder nodes
End of explanation
n_epochs = 1000
learning_rate = 0.01
reset_graph()
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()
n_epochs = 10
batch_size = 100
n_batches = int(np.ceil(m / batch_size))
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()
best_theta
Explanation: Mini-batch Gradient Descent
End of explanation
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")
best_theta
with tf.Session() as sess:
    saver.restore(sess, "/tmp/my_model_final.ckpt")
    best_theta_restored = theta.eval() # not shown in the book
np.allclose(best_theta, best_theta_restored)
Explanation: Saving and restoring a model
End of explanation
saver = tf.train.Saver({"weights": theta})
Explanation: If you want to have a saver that loads and restores theta with a different name, such as "weights":
End of explanation
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
np.allclose(best_theta, best_theta_restored)
Explanation: 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):
End of explanation
from IPython.display import clear_output, Image, display, HTML
def strip_consts(graph_def, max_const_size=32):
    Strip large constant values from graph_def.
    strip_def = tf.GraphDef()
    for n0 in graph_def.node:
        n = strip_def.node.add() 
        n.MergeFrom(n0)
        if n.op == 'Const':
            tensor = n.attr['value'].tensor
            size = len(tensor.tensor_content)
            if size > max_const_size:
                tensor.tensor_content = b"<stripped %d bytes>"%size
    return strip_def
def show_graph(graph_def, max_const_size=32):
    Visualize TensorFlow graph.
    if hasattr(graph_def, 'as_graph_def'):
        graph_def = graph_def.as_graph_def()
    strip_def = strip_consts(graph_def, max_const_size=max_const_size)
    code = 
        <script>
          function load() {{
            document.getElementById("{id}").pbtxt = {data};
          }}
        </script>
        <link rel="import" href="https://tensorboard.appspot.com/tf-graph-basic.build.html" onload=load()>
        <div style="height:600px">
          <tf-graph-basic id="{id}"></tf-graph-basic>
        </div>
    .format(data=repr(str(strip_def)), id='graph'+str(np.random.rand()))
    iframe = 
        <iframe seamless style="width:1200px;height:620px;border:0" srcdoc="{}"></iframe>
    .format(code.replace('"', '&quot;'))
    display(HTML(iframe))
show_graph(tf.get_default_graph())
Explanation: 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
End of explanation
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)
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()
mse_summary = tf.summary.scalar('MSE', mse)
file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())
n_epochs = 10
batch_size = 100
n_batches = int(np.ceil(m / batch_size))
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
file_writer.close()
best_theta
Explanation: Using TensorBoard
End of explanation
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")
with tf.name_scope("loss") as scope:
    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()
mse_summary = tf.summary.scalar('MSE', mse)
file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())
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)
print(error.op.name)
print(mse.op.name)
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)
Explanation: Name scopes
End of explanation
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")
Explanation: Modularity
An ugly flat code:
End of explanation
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")
file_writer = tf.summary.FileWriter("logs/relu1", tf.get_default_graph())
Explanation: Much better, using a function to build the ReLUs:
End of explanation
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
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()
Explanation: Even better using name scopes:
End of explanation
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")
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")
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")
reset_graph()
with tf.variable_scope("relu"):
    threshold = tf.get_variable("threshold", shape=(),
                                initializer=tf.constant_initializer(0.0))
with tf.variable_scope("relu", reuse=True):
    threshold = tf.get_variable("threshold")
with tf.variable_scope("relu") as scope:
    scope.reuse_variables()
    threshold = tf.get_variable("threshold")
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")
file_writer = tf.summary.FileWriter("logs/relu6", tf.get_default_graph())
file_writer.close()
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()
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")
file_writer = tf.summary.FileWriter("logs/relu9", tf.get_default_graph())
file_writer.close()
Explanation: Sharing Variables
Sharing a threshold variable the classic way, by defining it outside of the relu() function then passing it as a parameter:
End of explanation
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)
Explanation: Extra material
End of explanation
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())
Explanation: 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
End of explanation
class Const(object):
    def __init__(self, value):
        self.value = value
    def evaluate(self):
        return self.value
    def __str__(self):
        return str(self.value)
class Var(object):
    def __init__(self, init_value, name):
        self.value = init_value
        self.name = name
    def evaluate(self):
        return self.value
    def __str__(self):
        return self.name
class BinaryOperator(object):
    def __init__(self, a, b):
        self.a = a
        self.b = b
class Add(BinaryOperator):
    def evaluate(self):
        return self.a.evaluate() + self.b.evaluate()
    def __str__(self):
        return "{} + {}".format(self.a, self.b)
class Mul(BinaryOperator):
    def evaluate(self):
        return self.a.evaluate() * self.b.evaluate()
    def __str__(self):
        return "({}) * ({})".format(self.a, self.b)
x = Var(3, name="x")
y = Var(4, name="y")
f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2
print("f(x,y) =", f)
print("f(3,4) =", f.evaluate())
Explanation: Implementing a Home-Made Computation Graph
End of explanation
df_dx = Mul(Const(2), Mul(x, y))  # df/dx = 2xy
df_dy = Add(Mul(x, x), Const(1))  # df/dy = x² + 1
print("df/dx(3,4) =", df_dx.evaluate())
print("df/dy(3,4) =", df_dy.evaluate())
Explanation: Computing gradients
Mathematical differentiation
End of explanation
def gradients(func, vars_list, eps=0.0001):
    partial_derivatives = []
    base_func_eval = func.evaluate()
    for var in vars_list:
        original_value = var.value
        var.value = var.value + eps
        tweaked_func_eval = func.evaluate()
        var.value = original_value
        derivative = (tweaked_func_eval - base_func_eval) / eps
        partial_derivatives.append(derivative)
    return partial_derivatives
df_dx, df_dy = gradients(f, [x, y])
print("df/dx(3,4) =", df_dx)
print("df/dy(3,4) =", df_dy)
Explanation: Numerical differentiation
End of explanation
Const.derive = lambda self, var: Const(0)
Var.derive = lambda self, var: Const(1) if self is var else Const(0)
Add.derive = lambda self, var: Add(self.a.derive(var), self.b.derive(var))
Mul.derive = lambda self, var: Add(Mul(self.a, self.b.derive(var)), Mul(self.a.derive(var), self.b))
x = Var(3.0, name="x")
y = Var(4.0, name="y")
f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2
df_dx = f.derive(x)  # 2xy
df_dy = f.derive(y)  # x² + 1
print("df/dx(3,4) =", df_dx.evaluate())
print("df/dy(3,4) =", df_dy.evaluate())
Explanation: Symbolic differentiation
End of explanation
class DualNumber(object):
    def __init__(self, value=0.0, eps=0.0):
        self.value = value
        self.eps = eps
    def __add__(self, b):
        return DualNumber(self.value + self.to_dual(b).value,
                          self.eps + self.to_dual(b).eps)
    def __radd__(self, a):
        return self.to_dual(a).__add__(self)
    def __mul__(self, b):
        return DualNumber(self.value * self.to_dual(b).value,
                          self.eps * self.to_dual(b).value + self.value * self.to_dual(b).eps)
    def __rmul__(self, a):
        return self.to_dual(a).__mul__(self)
    def __str__(self):
        if self.eps:
            return "{:.1f} + {:.1f}ε".format(self.value, self.eps)
        else:
            return "{:.1f}".format(self.value)
    def __repr__(self):
        return str(self)
    @classmethod
    def to_dual(cls, n):
        if hasattr(n, "value"):
            return n
        else:
            return cls(n)
Explanation: Automatic differentiation (autodiff) – forward mode
End of explanation
3 + DualNumber(3, 4)
Explanation: $3 + (3 + 4 \epsilon) = 6 + 4\epsilon$
End of explanation
DualNumber(3, 4) * DualNumber(5, 7)
x.value = DualNumber(3.0)
y.value = DualNumber(4.0)
f.evaluate()
x.value = DualNumber(3.0, 1.0)  # 3 + ε
y.value = DualNumber(4.0)       # 4
df_dx = f.evaluate().eps
x.value = DualNumber(3.0)       # 3
y.value = DualNumber(4.0, 1.0)  # 4 + ε
df_dy = f.evaluate().eps
df_dx
df_dy
Explanation: $(3 + 4ε)\times(5 + 7ε) = 3 \times 5 + 3 \times 7ε + 4ε \times 5 + 4ε \times 7ε = 15 + 21ε + 20ε + 28ε^2 = 15 + 41ε + 28 \times 0 = 15 + 41ε$
End of explanation
class Const(object):
    def __init__(self, value):
        self.value = value
    def evaluate(self):
        return self.value
    def backpropagate(self, gradient):
        pass
    def __str__(self):
        return str(self.value)
class Var(object):
    def __init__(self, init_value, name):
        self.value = init_value
        self.name = name
        self.gradient = 0
    def evaluate(self):
        return self.value
    def backpropagate(self, gradient):
        self.gradient += gradient
    def __str__(self):
        return self.name
class BinaryOperator(object):
    def __init__(self, a, b):
        self.a = a
        self.b = b
class Add(BinaryOperator):
    def evaluate(self):
        self.value = self.a.evaluate() + self.b.evaluate()
        return self.value
    def backpropagate(self, gradient):
        self.a.backpropagate(gradient)
        self.b.backpropagate(gradient)
    def __str__(self):
        return "{} + {}".format(self.a, self.b)
class Mul(BinaryOperator):
    def evaluate(self):
        self.value = self.a.evaluate() * self.b.evaluate()
        return self.value
    def backpropagate(self, gradient):
        self.a.backpropagate(gradient * self.b.value)
        self.b.backpropagate(gradient * self.a.value)
    def __str__(self):
        return "({}) * ({})".format(self.a, self.b)
x = Var(3, name="x")
y = Var(4, name="y")
f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2
result = f.evaluate()
f.backpropagate(1.0)
print("f(x,y) =", f)
print("f(3,4) =", result)
print("df_dx =", x.gradient)
print("df_dy =", y.gradient)
Explanation: Autodiff – Reverse mode
End of explanation
reset_graph()
x = tf.Variable(3., name="x")
y = tf.Variable(4., name="y")
f = x*x*y + y + 2
gradients = tf.gradients(f, [x, y])
init = tf.global_variables_initializer()
with tf.Session() as sess:
    init.run()
    f_val, gradients_val = sess.run([f, gradients])
f_val, gradients_val
Explanation: Autodiff – reverse mode (using TensorFlow)
End of explanation
from sklearn.datasets import make_moons
m = 1000
X_moons, y_moons = make_moons(m, noise=0.1, random_state=42)
Explanation: 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:
End of explanation
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()
Explanation: Let's take a peek at the dataset:
End of explanation
X_moons_with_bias = np.c_[np.ones((m, 1)), X_moons]
Explanation: 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 $\mathbf{X}$:
End of explanation
X_moons_with_bias[:5]
Explanation: Let's check:
End of explanation
y_moons_column_vector = y_moons.reshape(-1, 1)
Explanation: Looks good. Now let's reshape y_train to make it a column vector (i.e. a 2D array with a single column):
End of explanation
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:]
Explanation: Now let's split the data into a training set and a test set:
End of explanation
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
Explanation: 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:
End of explanation
X_batch, y_batch = random_batch(X_train, y_train, 5)
X_batch
y_batch
Explanation: Let's look at a small batch:
End of explanation
reset_graph()
Explanation: 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.
End of explanation
n_inputs = 2
Explanation: The moons dataset has two input features, since each instance is a point on a plane (i.e., 2-Dimensional):
End of explanation
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))
Explanation: 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:
$\hat{p} = h_\mathbf{\theta}(\mathbf{x}) = \sigma(\mathbf{\theta}^T \cdot \mathbf{x})$
Recall that $\mathbf{\theta}$ 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} \cdot \mathbf{\theta})$
That's all we need to build the model:
End of explanation
y_proba = tf.sigmoid(logits)
Explanation: In fact, TensorFlow has a nice function tf.sigmoid() that we can use to simplify the last line of the previous code:
End of explanation
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))
Explanation: As we saw in chapter 4, the log loss is a good cost function to use for Logistic Regression:
$J(\mathbf{\theta}) = -\dfrac{1}{m} \sum\limits_{i=1}^{m}{\left[ y^{(i)} log\left(\hat{p}^{(i)}\right) + (1 - y^{(i)}) log\left(1 - \hat{p}^{(i)}\right)\right]}$
One option is to implement it ourselves:
End of explanation
loss = tf.losses.log_loss(y, y_proba)  # uses epsilon = 1e-7 by default
Explanation: But we might as well use TensorFlow's tf.losses.log_loss() function:
End of explanation
learning_rate = 0.01
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(loss)
Explanation: The rest is pretty standard: let's create the optimizer and tell it to minimize the cost function:
End of explanation
init = tf.global_variables_initializer()
Explanation: All we need now (in this minimal version) is the variable initializer:
End of explanation
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})
Explanation: 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:
End of explanation
y_proba_val[:5]
Explanation: 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:
End of explanation
y_pred = (y_proba_val >= 0.5)
y_pred[:5]
Explanation: 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:
End of explanation
from sklearn.metrics import precision_score, recall_score
precision_score(y_test, y_pred)
recall_score(y_test, y_pred)
Explanation: 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:
End of explanation
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()
Explanation: Let's plot these predictions to see what they look like:
End of explanation
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]
Explanation: 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.
End of explanation
X_train_enhanced[:5]
Explanation: This is what the "enhanced" training set looks like:
End of explanation
reset_graph()
Explanation: Ok, next let's reset the default graph:
End of explanation
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
Explanation: 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).
End of explanation
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)
Explanation: Let's create a little function to get the name of the log directory to save the summaries for Tensorboard:
End of explanation
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())
Explanation: 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:
End of explanation
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)
Explanation: 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.
End of explanation
y_pred = (y_proba_val >= 0.5)
precision_score(y_test, y_pred)
recall_score(y_test, y_pred)
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()
Explanation: Once again, we can make predictions by just classifying as positive all the instances whose estimated probability is greater or equal to 0.5:
End of explanation
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))
Explanation: 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.
End of explanation
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