Chapter 9 – Up and running with TensorFlow
This notebook contains all the sample code and solutions to the exercices in chapter 9.
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)
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]:
f
Out[3]:
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]:
In [14]:
reset_graph()
x1 = tf.Variable(1)
x1.graph is tf.get_default_graph()
Out[14]:
In [15]:
graph = tf.Graph()
with graph.as_default():
x2 = tf.Variable(2)
x2.graph is graph
Out[15]:
In [16]:
x2.graph is tf.get_default_graph()
Out[16]:
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
In [18]:
with tf.Session() as sess:
y_val, z_val = sess.run([y, z])
print(y_val) # 10
print(z_val) # 15
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]:
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)
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])
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)
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()
In [26]:
best_theta
Out[26]:
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)
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]:
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))
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)
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)
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)
In [42]:
print(B_val_2)
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]:
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")
In [51]:
best_theta
Out[51]:
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
In [53]:
np.allclose(best_theta, best_theta_restored)
Out[53]:
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
In [56]:
np.allclose(best_theta, best_theta_restored)
Out[56]:
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.
In [57]:
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('"', '"'))
display(HTML(iframe))
In [58]:
show_graph(tf.get_default_graph())
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]:
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)
In [70]:
print(error.op.name)
In [71]:
print(mse.op.name)
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)
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()
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)
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").
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())
In [91]:
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())
In [92]:
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())
In [93]:
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)
In [94]:
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())
In [95]:
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)
$3 + (3 + 4 \epsilon) = 6 + 4\epsilon$
In [96]:
3 + DualNumber(3, 4)
Out[96]:
$(3 + 4ε)\times(5 + 7ε) = 3 \times 5 + 3 \times 7ε + 4ε \times 5 + 4ε \times 7ε = 15 + 21ε + 20ε + 28ε^2 = 15 + 41ε + 28 \times 0 = 15 + 41ε$
In [97]:
DualNumber(3, 4) * DualNumber(5, 7)
Out[97]:
In [98]:
x.value = DualNumber(3.0)
y.value = DualNumber(4.0)
f.evaluate()
Out[98]:
In [99]:
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
In [100]:
df_dx
Out[100]:
In [101]:
df_dy
Out[101]:
In [102]:
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)
In [103]:
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
Out[103]:
See appendix A.
First, let's create the moons dataset using Scikit-Learn's make_moons() function:
In [104]:
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 [105]:
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 [106]:
X_moons_with_bias = np.c_[np.ones((m, 1)), X_moons]
Let's check:
In [107]:
X_moons_with_bias[:5]
Out[107]:
Looks good. Now let's reshape y_train to make it a column vector (i.e. a 2D array with a single column):
In [108]:
y_moons_column_vector = y_moons.reshape(-1, 1)
Now let's split the data into a training set and a test set:
In [109]:
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 [110]:
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 [111]:
X_batch, y_batch = random_batch(X_train, y_train, 5)
X_batch
Out[111]:
In [112]:
y_batch
Out[112]:
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 [113]:
reset_graph()
The moons dataset has two input features, since each instance is a point on a plane (i.e., 2-Dimensional):
In [114]:
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:
$\hat{p} = h_\mathbf{\theta}(\mathbf{x}) = \sigma(\mathbf{\theta}^T \cdot \mathbf{x})$
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:
In [115]:
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 [116]:
y_proba = tf.sigmoid(logits)
As we saw in chapter 4, the log loss is a good cost function to use for Logistic Regression:
$J(\mathbf{\theta}) = -\dfrac{1}{m} \sum\limits_{i=1}^{m}{\left[ y^{(i)} log\left(\hat{p}^{(i)}\right) + (1 - y^{(i)}) log\left(1 - \hat{p}^{(i)}\right)\right]}$
One option is to implement it ourselves:
In [117]:
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 [118]:
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 [119]:
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 [120]:
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 [121]:
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})
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 [122]:
y_proba_val[:5]
Out[122]:
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 [123]:
y_pred = (y_proba_val >= 0.5)
y_pred[:5]
Out[123]:
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 [124]:
from sklearn.metrics import precision_score, recall_score
precision_score(y_test, y_pred)
Out[124]:
In [125]:
recall_score(y_test, y_pred)
Out[125]:
Let's plot these predictions to see what they look like:
In [126]:
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:
logistic_regression() function that can be reused easily.Saver at regular intervals during training, and save the final model at the end of training.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 [127]:
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 [128]:
X_train_enhanced[:5]
Out[128]:
Ok, next let's reset the default graph:
In [129]:
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 [130]:
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 [131]:
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 [132]:
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 [133]:
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)
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 [134]:
y_pred = (y_proba_val >= 0.5)
In [135]:
precision_score(y_test, y_pred)
Out[135]:
In [136]:
recall_score(y_test, y_pred)
Out[136]:
In [137]:
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_logsNow 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.
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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))
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.
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