SDS-2.2, Scalable Data Science

This is used in a non-profit educational setting with kind permission of Adam Breindel. This is not licensed by Adam for use in a for-profit setting. Please contact Adam directly at [email protected] to request or report such use cases or abuses. A few minor modifications and additional mathematical statistical pointers have been added by Raazesh Sainudiin when teaching PhD students in Uppsala University.

Try out the first ConvNet -- the one we looked at earlier.

This code is the same, but we'll run to 20 epochs so we can get a better feel for fitting/validation/overfitting trend.

from keras.utils import to_categorical
import sklearn.datasets

train_libsvm = "/dbfs/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt"
test_libsvm = "/dbfs/databricks-datasets/mnist-digits/data-001/mnist-digits-test.txt"

X_train, y_train = sklearn.datasets.load_svmlight_file(train_libsvm, n_features=784)
X_train = X_train.toarray()

X_test, y_test = sklearn.datasets.load_svmlight_file(test_libsvm, n_features=784)
X_test = X_test.toarray()

X_train = X_train.reshape( (X_train.shape[0], 28, 28, 1) )
X_train = X_train.astype('float32')
X_train /= 255
y_train = to_categorical(y_train, num_classes=10)

X_test = X_test.reshape( (X_test.shape[0], 28, 28, 1) )
X_test = X_test.astype('float32')
X_test /= 255
y_test = to_categorical(y_test, num_classes=10)

from keras.models import Sequential
from keras.layers import Dense, Dropout, Activation, Flatten, Conv2D, MaxPooling2D

model = Sequential()

model.add(Conv2D(8, # number of kernels 
                (4, 4), # kernel size
                padding='valid', # no padding; output will be smaller than input
                input_shape=(28, 28, 1)))

model.add(Activation('relu'))

model.add(MaxPooling2D(pool_size=(2,2)))

model.add(Flatten())
model.add(Dense(128))
model.add(Activation('relu')) # alternative syntax for applying activation

model.add(Dense(10))
model.add(Activation('softmax'))

model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

history = model.fit(X_train, y_train, batch_size=128, epochs=20, verbose=2, validation_split=0.1)

scores = model.evaluate(X_test, y_test, verbose=1)

print
for i in range(len(model.metrics_names)):
    print("%s: %f" % (model.metrics_names[i], scores[i]))

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
fig.set_size_inches((5,5))
plt.plot(history.history['loss'])
plt.plot(history.history['val_loss'])
plt.title('model loss')
plt.ylabel('loss')
plt.xlabel('epoch')
plt.legend(['train', 'val'], loc='upper left')
display(fig)

Next, let's try adding another convolutional layer:

model = Sequential()

model.add(Conv2D(8, # number of kernels 
                        (4, 4), # kernel size
                        padding='valid',
                        input_shape=(28, 28, 1)))

model.add(Activation('relu'))

model.add(Conv2D(8, (4, 4))) # <-- additional Conv layer
model.add(Activation('relu'))

model.add(MaxPooling2D(pool_size=(2,2)))

model.add(Flatten())
model.add(Dense(128))
model.add(Activation('relu'))

model.add(Dense(10))
model.add(Activation('softmax'))

model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

history = model.fit(X_train, y_train, batch_size=128, epochs=15, verbose=2, validation_split=0.1)

scores = model.evaluate(X_test, y_test, verbose=1)

print
for i in range(len(model.metrics_names)):
    print("%s: %f" % (model.metrics_names[i], scores[i]))

Still Overfitting

We're making progress on our test error -- about 99% -- but just a bit for all the additional time, due to the network overfitting the data.

There are a variety of techniques we can take to counter this -- forms of regularization.

Let's try a relatively simple solution solution that works surprisingly well: add a pair of Dropout filters, a layer that randomly omits a fraction of neurons from each training batch (thus exposing each neuron to only part of the training data).

We'll add more convolution kernels but shrink them to 3x3 as well.

model = Sequential()

model.add(Conv2D(32, # number of kernels 
                        (3, 3), # kernel size
                        padding='valid',
                        input_shape=(28, 28, 1)))

model.add(Activation('relu'))

model.add(Conv2D(32, (3, 3)))
model.add(Activation('relu'))

model.add(MaxPooling2D(pool_size=(2,2)))

model.add(Dropout(0.25))
model.add(Flatten())
model.add(Dense(128))
model.add(Activation('relu'))

model.add(Dropout(0.5))
model.add(Dense(10))
model.add(Activation('softmax'))

model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
history = model.fit(X_train, y_train, batch_size=128, epochs=15, verbose=2)

scores = model.evaluate(X_test, y_test, verbose=2)

print
for i in range(len(model.metrics_names)):
    print("%s: %f" % (model.metrics_names[i], scores[i]))

Lab Wrapup

From the last lab, you should have a test accuracy of over 99.1%

For one more activity, try changing the optimizer to old-school "sgd" -- just to see how far we've come with these modern gradient descent techniques in the last few years.

Accuracy will end up noticeably worse ... about 96-97% test accuracy. Two key takeaways:

• Without a good optimizer, even a very powerful network design may not achieve results
• In fact, we could replace the word "optimizer" there with
  • initialization
  • activation
  • regularization
  • (etc.)
• All of these elements we've been working with operate together in a complex way to determine final performance