Keras is a minimalist, highly modular neural networks library, written in Python and capable of running on top of either TensorFlow or Theano. It was developed with a focus on enabling fast experimentation. Being able to go from idea to result with the least possible delay is key to doing good research. ref: https://keras.io/
Keras (κέρας) means horn in Greek. It is a reference to a literary image from ancient Greek and Latin literature, first found in the Odyssey, where dream spirits (Oneiroi, singular Oneiros) are divided between those who deceive men with false visions, who arrive to Earth through a gate of ivory, and those who announce a future that will come to pass, who arrive through a gate of horn. It's a play on the words κέρας (horn) / κραίνω (fulfill), and ἐλέφας (ivory) / ἐλεφαίρομαι (deceive).
Keras was initially developed as part of the research effort of project ONEIROS (Open-ended Neuro-Electronic Intelligent Robot Operating System).
"Oneiroi are beyond our unravelling --who can be sure what tale they tell? Not all that men look for comes to pass. Two gates there are that give passage to fleeting Oneiroi; one is made of horn, one of ivory. The Oneiroi that pass through sawn ivory are deceitful, bearing a message that will not be fulfilled; those that come out through polished horn have truth behind them, to be accomplished for men who see them." Homer, Odyssey 19. 562 ff (Shewring translation).
See: Data Description
In [1]:
from kaggle_data import load_data, preprocess_data, preprocess_labels
X_train, labels = load_data('data/kaggle_ottogroup/train.csv', train=True)
X_train, scaler = preprocess_data(X_train)
Y_train, encoder = preprocess_labels(labels)
X_test, ids = load_data('data/kaggle_ottogroup/test.csv', train=False)
X_test, _ = preprocess_data(X_test, scaler)
nb_classes = Y_train.shape[1]
print(nb_classes, 'classes')
dims = X_train.shape[1]
print(dims, 'dims')
In [2]:
from keras.models import Sequential
from keras.layers import Dense, Activation
In [5]:
dims = X_train.shape[1]
print(dims, 'dims')
print("Building model...")
nb_classes = Y_train.shape[1]
print(nb_classes, 'classes')
model = Sequential()
model.add(Dense(nb_classes, input_shape=(dims,)))
model.add(Activation('softmax'))
model.compile(optimizer='sgd', loss='categorical_crossentropy')
model.fit(X_train, Y_train)
Out[5]:
Simplicity is pretty impressive right? :)
Now lets understand:
The core data structure of Keras is a model, a way to organize layers. The main type of model is the Sequential model, a linear stack of layers.
What we did here is stacking a Fully Connected (Dense) layer of trainable weights from the input to the output and an Activation layer on top of the weights layer.
from keras.layers.core import Dense
Dense(units, activation=None, use_bias=True,
kernel_initializer='glorot_uniform', bias_initializer='zeros',
kernel_regularizer=None, bias_regularizer=None,
activity_regularizer=None, kernel_constraint=None, bias_constraint=None)
units: int > 0.
init: name of initialization function for the weights of the layer (see initializations), or alternatively, Theano function to use for weights initialization. This parameter is only relevant if you don't pass a weights argument.
activation: name of activation function to use (see activations), or alternatively, elementwise Theano function. If you don't specify anything, no activation is applied (ie. "linear" activation: a(x) = x).
weights: list of Numpy arrays to set as initial weights. The list should have 2 elements, of shape (input_dim, output_dim) and (output_dim,) for weights and biases respectively.
kernel_regularizer: instance of WeightRegularizer (eg. L1 or L2 regularization), applied to the main weights matrix.
bias_regularizer: instance of WeightRegularizer, applied to the bias.
activity_regularizer: instance of ActivityRegularizer, applied to the network output.
kernel_constraint: instance of the constraints module (eg. maxnorm, nonneg), applied to the main weights matrix.
bias_constraint: instance of the constraints module, applied to the bias.
use_bias: whether to include a bias (i.e. make the layer affine rather than linear).
keras.layers.core.Flatten()keras.layers.core.Reshape(target_shape)keras.layers.core.Permute(dims)model = Sequential()
model.add(Permute((2, 1), input_shape=(10, 64)))
# now: model.output_shape == (None, 64, 10)
# note: `None` is the batch dimension
keras.layers.core.Lambda(function, output_shape=None, arguments=None)keras.layers.core.ActivityRegularization(l1=0.0, l2=0.0)Credits: Yam Peleg (@Yampeleg)
from keras.layers.core import Activation
Activation(activation)
Supported Activations : [https://keras.io/activations/]
Advanced Activations: [https://keras.io/layers/advanced-activations/]
If you need to, you can further configure your optimizer. A core principle of Keras is to make things reasonably simple, while allowing the user to be fully in control when they need to (the ultimate control being the easy extensibility of the source code). Here we used SGD (stochastic gradient descent) as an optimization algorithm for our trainable weights.
What we did here is nice, however in the real world it is not useable because of overfitting. Lets try and solve it with cross validation.
In overfitting, a statistical model describes random error or noise instead of the underlying relationship. Overfitting occurs when a model is excessively complex, such as having too many parameters relative to the number of observations.
A model that has been overfit has poor predictive performance, as it overreacts to minor fluctuations in the training data.
To avoid overfitting, we will first split out data to training set and test set and test out model on the test set. Next: we will use two of keras's callbacks EarlyStopping and ModelCheckpoint
Let's see first the model we implemented
In [7]:
model.summary()
In [8]:
from sklearn.model_selection import train_test_split
from keras.callbacks import EarlyStopping, ModelCheckpoint
In [11]:
X_train, X_val, Y_train, Y_val = train_test_split(X_train, Y_train, test_size=0.15, random_state=42)
fBestModel = 'best_model.h5'
early_stop = EarlyStopping(monitor='val_loss', patience=4, verbose=1)
best_model = ModelCheckpoint(fBestModel, verbose=0, save_best_only=True)
model.fit(X_train, Y_train, validation_data = (X_val, Y_val), epochs=20,
batch_size=128, verbose=True, callbacks=[best_model, early_stop])
Out[11]:
So, how hard can it be to build a Multi-Layer percepton with keras? It is baiscly the same, just add more layers!
In [12]:
model = Sequential()
model.add(Dense(100, input_shape=(dims,)))
model.add(Dense(nb_classes))
model.add(Activation('softmax'))
model.compile(optimizer='sgd', loss='categorical_crossentropy')
model.summary()
In [13]:
model.fit(X_train, Y_train, validation_data = (X_val, Y_val), epochs=20,
batch_size=128, verbose=True)
Out[13]:
Your Turn!
Take couple of minutes and Try and optimize the number of layers and the number of parameters in the layers to get the best results.
In [ ]:
model = Sequential()
model.add(Dense(100, input_shape=(dims,)))
# ...
# ...
# Play with it! add as much layers as you want! try and get better results.
model.add(Dense(nb_classes))
model.add(Activation('softmax'))
model.compile(optimizer='sgd', loss='categorical_crossentropy')
model.fit(X_train, Y_train, validation_data = (X_val, Y_val), epochs=20,
batch_size=128, verbose=True)
Building a question answering system, an image classification model, a Neural Turing Machine, a word2vec embedder or any other model is just as fast. The ideas behind deep learning are simple, so why should their implementation be painful?
Much has been studied about the depth of neural nets. Is has been proven mathematically[1] and empirically that convolutional neural network benifit from depth!
[1] - On the Expressive Power of Deep Learning: A Tensor Analysis - Cohen, et al 2015
One much quoted theorem about neural network states that:
Universal approximation theorem states[1] that a feed-forward network with a single hidden layer containing a finite number of neurons (i.e., a multilayer perceptron), can approximate continuous functions on compact subsets of $\mathbb{R}^n$, under mild assumptions on the activation function. The theorem thus states that simple neural networks can represent a wide variety of interesting functions when given appropriate parameters; however, it does not touch upon the algorithmic learnability of those parameters.
[1] - Approximation Capabilities of Multilayer Feedforward Networks - Kurt Hornik 1991