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import keras
keras.__version__
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This notebook contains the code samples found in Chapter 3, Section 5 of Deep Learning with Python. Note that the original text features far more content, in particular further explanations and figures: in this notebook, you will only find source code and related comments.
Two-class classification, or binary classification, may be the most widely applied kind of machine learning problem. In this example, we will learn to classify movie reviews into "positive" reviews and "negative" reviews, just based on the text content of the reviews.
We'll be working with "IMDB dataset", a set of 50,000 highly-polarized reviews from the Internet Movie Database. They are split into 25,000 reviews for training and 25,000 reviews for testing, each set consisting in 50% negative and 50% positive reviews.
Why do we have these two separate training and test sets? You should never test a machine learning model on the same data that you used to train it! Just because a model performs well on its training data doesn't mean that it will perform well on data it has never seen, and what you actually care about is your model's performance on new data (since you already know the labels of your training data -- obviously you don't need your model to predict those). For instance, it is possible that your model could end up merely memorizing a mapping between your training samples and their targets -- which would be completely useless for the task of predicting targets for data never seen before. We will go over this point in much more detail in the next chapter.
Just like the MNIST dataset, the IMDB dataset comes packaged with Keras. It has already been preprocessed: the reviews (sequences of words) have been turned into sequences of integers, where each integer stands for a specific word in a dictionary.
The following code will load the dataset (when you run it for the first time, about 80MB of data will be downloaded to your machine):
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from keras.datasets import imdb
(train_data, train_labels), (test_data, test_labels) = imdb.load_data(num_words=10000)
The argument num_words=10000 means that we will only keep the top 10,000 most frequently occurring words in the training data. Rare words
will be discarded. This allows us to work with vector data of manageable size.
The variables train_data and test_data are lists of reviews, each review being a list of word indices (encoding a sequence of words).
train_labels and test_labels are lists of 0s and 1s, where 0 stands for "negative" and 1 stands for "positive":
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train_data[0]
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train_labels[0]
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Since we restricted ourselves to the top 10,000 most frequent words, no word index will exceed 10,000:
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max([max(sequence) for sequence in train_data])
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For kicks, here's how you can quickly decode one of these reviews back to English words:
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# word_index is a dictionary mapping words to an integer index
word_index = imdb.get_word_index()
# We reverse it, mapping integer indices to words
reverse_word_index = dict([(value, key) for (key, value) in word_index.items()])
# We decode the review; note that our indices were offset by 3
# because 0, 1 and 2 are reserved indices for "padding", "start of sequence", and "unknown".
decoded_review = ' '.join([reverse_word_index.get(i - 3, '?') for i in train_data[0]])
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decoded_review
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We cannot feed lists of integers into a neural network. We have to turn our lists into tensors. There are two ways we could do that:
(samples, word_indices),
then use as first layer in our network a layer capable of handling such integer tensors (the Embedding layer, which we will cover in
detail later in the book).[3, 5] into a 10,000-dimensional vector that would be all-zeros except for indices 3 and 5, which would be ones. Then we could use as
first layer in our network a Dense layer, capable of handling floating point vector data.We will go with the latter solution. Let's vectorize our data, which we will do manually for maximum clarity:
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import numpy as np
def vectorize_sequences(sequences, dimension=10000):
# Create an all-zero matrix of shape (len(sequences), dimension)
results = np.zeros((len(sequences), dimension))
for i, sequence in enumerate(sequences):
results[i, sequence] = 1. # set specific indices of results[i] to 1s
return results
# Our vectorized training data
x_train = vectorize_sequences(train_data)
# Our vectorized test data
x_test = vectorize_sequences(test_data)
Here's what our samples look like now:
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x_train[0]
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We should also vectorize our labels, which is straightforward:
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# Our vectorized labels
y_train = np.asarray(train_labels).astype('float32')
y_test = np.asarray(test_labels).astype('float32')
Now our data is ready to be fed into a neural network.
Our input data is simply vectors, and our labels are scalars (1s and 0s): this is the easiest setup you will ever encounter. A type of
network that performs well on such a problem would be a simple stack of fully-connected (Dense) layers with relu activations: Dense(16,
activation='relu')
The argument being passed to each Dense layer (16) is the number of "hidden units" of the layer. What's a hidden unit? It's a dimension
in the representation space of the layer. You may remember from the previous chapter that each such Dense layer with a relu activation implements
the following chain of tensor operations:
output = relu(dot(W, input) + b)
Having 16 hidden units means that the weight matrix W will have shape (input_dimension, 16), i.e. the dot product with W will project the
input data onto a 16-dimensional representation space (and then we would add the bias vector b and apply the relu operation). You can
intuitively understand the dimensionality of your representation space as "how much freedom you are allowing the network to have when
learning internal representations". Having more hidden units (a higher-dimensional representation space) allows your network to learn more
complex representations, but it makes your network more computationally expensive and may lead to learning unwanted patterns (patterns that
will improve performance on the training data but not on the test data).
There are two key architecture decisions to be made about such stack of dense layers:
In the next chapter, you will learn formal principles to guide you in making these choices.
For the time being, you will have to trust us with the following architecture choice:
two intermediate layers with 16 hidden units each,
and a third layer which will output the scalar prediction regarding the sentiment of the current review.
The intermediate layers will use relu as their "activation function",
and the final layer will use a sigmoid activation so as to output a probability
(a score between 0 and 1, indicating how likely the sample is to have the target "1", i.e. how likely the review is to be positive).
A relu (rectified linear unit) is a function meant to zero-out negative values,
while a sigmoid "squashes" arbitrary values into the [0, 1] interval, thus outputting something that can be interpreted as a probability.
Here's what our network looks like:
And here's the Keras implementation, very similar to the MNIST example you saw previously:
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from keras import models
from keras import layers
model = models.Sequential()
model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
model.add(layers.Dense(16, activation='relu'))
model.add(layers.Dense(1, activation='sigmoid'))
Lastly, we need to pick a loss function and an optimizer. Since we are facing a binary classification problem and the output of our network
is a probability (we end our network with a single-unit layer with a sigmoid activation), is it best to use the binary_crossentropy loss.
It isn't the only viable choice: you could use, for instance, mean_squared_error. But crossentropy is usually the best choice when you
are dealing with models that output probabilities. Crossentropy is a quantity from the field of Information Theory, that measures the "distance"
between probability distributions, or in our case, between the ground-truth distribution and our predictions.
Here's the step where we configure our model with the rmsprop optimizer and the binary_crossentropy loss function. Note that we will
also monitor accuracy during training.
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model.compile(optimizer='rmsprop',
loss='binary_crossentropy',
metrics=['accuracy'])
We are passing our optimizer, loss function and metrics as strings, which is possible because rmsprop, binary_crossentropy and
accuracy are packaged as part of Keras. Sometimes you may want to configure the parameters of your optimizer, or pass a custom loss
function or metric function. This former can be done by passing an optimizer class instance as the optimizer argument:
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from keras import optimizers
model.compile(optimizer=optimizers.RMSprop(lr=0.001),
loss='binary_crossentropy',
metrics=['accuracy'])
The latter can be done by passing function objects as the loss or metrics arguments:
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from keras import losses
from keras import metrics
model.compile(optimizer=optimizers.RMSprop(lr=0.001),
loss=losses.binary_crossentropy,
metrics=[metrics.binary_accuracy])
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x_val = x_train[:10000]
partial_x_train = x_train[10000:]
y_val = y_train[:10000]
partial_y_train = y_train[10000:]
We will now train our model for 20 epochs (20 iterations over all samples in the x_train and y_train tensors), in mini-batches of 512
samples. At this same time we will monitor loss and accuracy on the 10,000 samples that we set apart. This is done by passing the
validation data as the validation_data argument:
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history = model.fit(partial_x_train,
partial_y_train,
epochs=20,
batch_size=512,
validation_data=(x_val, y_val))
On CPU, this will take less than two seconds per epoch -- training is over in 20 seconds. At the end of every epoch, there is a slight pause as the model computes its loss and accuracy on the 10,000 samples of the validation data.
Note that the call to model.fit() returns a History object. This object has a member history, which is a dictionary containing data
about everything that happened during training. Let's take a look at it:
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history_dict = history.history
history_dict.keys()
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It contains 4 entries: one per metric that was being monitored, during training and during validation. Let's use Matplotlib to plot the training and validation loss side by side, as well as the training and validation accuracy:
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import matplotlib.pyplot as plt
acc = history.history['acc']
val_acc = history.history['val_acc']
loss = history.history['loss']
val_loss = history.history['val_loss']
epochs = range(1, len(acc) + 1)
# "bo" is for "blue dot"
plt.plot(epochs, loss, 'bo', label='Training loss')
# b is for "solid blue line"
plt.plot(epochs, val_loss, 'b', label='Validation loss')
plt.title('Training and validation loss')
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.legend()
plt.show()
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plt.clf() # clear figure
acc_values = history_dict['acc']
val_acc_values = history_dict['val_acc']
plt.plot(epochs, acc, 'bo', label='Training acc')
plt.plot(epochs, val_acc, 'b', label='Validation acc')
plt.title('Training and validation accuracy')
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.legend()
plt.show()
The dots are the training loss and accuracy, while the solid lines are the validation loss and accuracy. Note that your own results may vary slightly due to a different random initialization of your network.
As you can see, the training loss decreases with every epoch and the training accuracy increases with every epoch. That's what you would expect when running gradient descent optimization -- the quantity you are trying to minimize should get lower with every iteration. But that isn't the case for the validation loss and accuracy: they seem to peak at the fourth epoch. This is an example of what we were warning against earlier: a model that performs better on the training data isn't necessarily a model that will do better on data it has never seen before. In precise terms, what you are seeing is "overfitting": after the second epoch, we are over-optimizing on the training data, and we ended up learning representations that are specific to the training data and do not generalize to data outside of the training set.
In this case, to prevent overfitting, we could simply stop training after three epochs. In general, there is a range of techniques you can leverage to mitigate overfitting, which we will cover in the next chapter.
Let's train a new network from scratch for four epochs, then evaluate it on our test data:
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model = models.Sequential()
model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
model.add(layers.Dense(16, activation='relu'))
model.add(layers.Dense(1, activation='sigmoid'))
model.compile(optimizer='rmsprop',
loss='binary_crossentropy',
metrics=['accuracy'])
model.fit(x_train, y_train, epochs=4, batch_size=512)
results = model.evaluate(x_test, y_test)
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results
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Our fairly naive approach achieves an accuracy of 88%. With state-of-the-art approaches, one should be able to get close to 95%.
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model.predict(x_test)
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As you can see, the network is very confident for some samples (0.99 or more, or 0.01 or less) but less confident for others (0.6, 0.4).
mse loss function instead of binary_crossentropy.tanh activation (an activation that was popular in the early days of neural networks) instead of relu.These experiments will help convince you that the architecture choices we have made are all fairly reasonable, although they can still be improved!
Here's what you should take away from this example:
Dense layers with relu activations can solve a wide range of problems (including sentiment classification), and you will
likely use them frequently.Dense layer with 1 unit and a sigmoid activation,
i.e. the output of your network should be a scalar between 0 and 1, encoding a probability.binary_crossentropy.rmsprop optimizer is generally a good enough choice of optimizer, whatever your problem. That's one less thing for you to worry
about.