I can calculate the motion of heavenly bodies but not the madness of people. -Isaac Newton

## A Simple Convolutional Neural Network for The Binary Outcome

Since CNN(Convolutional Neural Networks) have achieved a tremendous success in various challenging applications, e.g. image or digit recognitions, one might wonder how to employ CNNs in classification problems with binary outcomes.

Below is an example showing how to use a simple 1D convolutional neural network to predict credit card defaults.

```### LOAD PACKAGES
from numpy.random import seed
from sklearn.preprocessing import minmax_scale
from keras.layers.convolutional import Conv1D, MaxPooling1D
from keras.optimizers import SGD
from keras.models import Sequential
from keras.layers import Dense, Flatten

### PREPARE THE DATA
Y = df[df.CARDHLDR == 1].DEFAULT
X = minmax_scale(df[df.CARDHLDR == 1].ix[:, 2:12], axis = 0)
y_train = Y.values
x_train = X.reshape(X.shape[0], X.shape[1], 1)

### FIT A 1D CONVOLUTIONAL NEURAL NETWORK
seed(2017)
conv = Sequential()
conv.add(Conv1D(20, 4, input_shape = x_train.shape[1:3], activation = 'relu'))
sgd = SGD(lr = 0.1, momentum = 0.9, decay = 0, nesterov = False)
conv.compile(loss = 'binary_crossentropy', optimizer = sgd, metrics = ['accuracy'])
conv.fit(x_train, y_train, batch_size = 500, epochs = 100, verbose = 0)
```

Considering that 1D is the special case of 2D, we can also solve the same problem with a 2D convolutional neural network by changing the input shape, as shown below.

```from numpy.random import seed
from sklearn.preprocessing import minmax_scale
from keras_diagram import ascii
from keras.layers.convolutional import Conv2D, MaxPooling2D
from keras.optimizers import SGD
from keras.models import Sequential
from keras.layers import Dense, Flatten

Y = df[df.CARDHLDR == 1].DEFAULT
X = minmax_scale(df[df.CARDHLDR == 1].ix[:, 2:12], axis = 0)
y_train = Y.values
x_train = X.reshape(X.shape[0], 1, X.shape[1], 1)

seed(2017)
conv = Sequential()
conv.add(Conv2D(20, (1, 4), input_shape = x_train.shape[1:4], activation = 'relu'))
sgd = SGD(lr = 0.1, momentum = 0.9, decay = 0, nesterov = False)
conv.compile(loss = 'binary_crossentropy', optimizer = sgd, metrics = ['accuracy'])
conv.fit(x_train, y_train, batch_size = 500, epochs = 100, verbose = 0)
```

Written by statcompute

April 2, 2017 at 11:45 pm

Tagged with , , ,

## Autoencoder for Dimensionality Reduction

We often use ICA or PCA to extract features from the high-dimensional data. The autoencoder is another interesting algorithm to achieve the same purpose in the context of Deep Learning.

with the purpose of learning a function to approximate the input data itself such that F(X) = X, an autoencoder consists of two parts, namely encoder and decoder. While the encoder aims to compress the original input data into a low-dimensional representation, the decoder tries to reconstruct the original input data based on the low-dimension representation generated by the encoder. As a result, the autoencoder has been widely used to remove the data noise as well to reduce the data dimension.

First of all, we will show the basic structure of an autoencoder with 1-layer encoder and 1-layer decoder, as below. In the example, we will compress the input data with 10 columns into a compressed on with 3 columns.

```from pandas import read_csv, DataFrame
from numpy.random import seed
from sklearn.preprocessing import minmax_scale
from sklearn.model_selection import train_test_split
from keras.layers import Input, Dense
from keras.models import Model

Y = df[df.CARDHLDR == 1].DEFAULTS
X = df[df.CARDHLDR == 1].ix[:, 2:12]
# SCALE EACH FEATURE INTO [0, 1] RANGE
sX = minmax_scale(X, axis = 0)
ncol = sX.shape[1]
X_train, X_test, Y_train, Y_test = train_test_split(sX, Y, train_size = 0.5, random_state = seed(2017))

### AN EXAMPLE OF SIMPLE AUTOENCODER ###
# InputLayer (None, 10)
#      Dense (None, 5)
#      Dense (None, 10)

input_dim = Input(shape = (ncol, ))
# DEFINE THE DIMENSION OF ENCODER ASSUMED 3
encoding_dim = 3
# DEFINE THE ENCODER LAYER
encoded = Dense(encoding_dim, activation = 'relu')(input_dim)
# DEFINE THE DECODER LAYER
decoded = Dense(ncol, activation = 'sigmoid')(encoded)
# COMBINE ENCODER AND DECODER INTO AN AUTOENCODER MODEL
autoencoder = Model(input = input_dim, output = decoded)
# CONFIGURE AND TRAIN THE AUTOENCODER
autoencoder.fit(X_train, X_train, nb_epoch = 50, batch_size = 100, shuffle = True, validation_data = (X_test, X_test))
# THE ENCODER TO EXTRACT THE REDUCED DIMENSION FROM THE ABOVE AUTOENCODER
encoder = Model(input = input_dim, output = encoded)
encoded_input = Input(shape = (encoding_dim, ))
encoded_out = encoder.predict(X_test)
encoded_out[0:2]
#array([[ 0.        ,  1.26510417,  1.62803197],
#       [ 2.32508397,  0.99735016,  2.06461048]], dtype=float32)
```

In the next example, we will relax the constraint of layers and employ a stack of layers to achievement the same purpose as above.

```### AN EXAMPLE OF DEEP AUTOENCODER WITH MULTIPLE LAYERS
# InputLayer (None, 10)
#      Dense (None, 20)
#      Dense (None, 10)
#      Dense (None, 5)
#      Dense (None, 3)
#      Dense (None, 5)
#      Dense (None, 10)
#      Dense (None, 20)
#      Dense (None, 10)

input_dim = Input(shape = (ncol, ))
# DEFINE THE DIMENSION OF ENCODER ASSUMED 3
encoding_dim = 3
# DEFINE THE ENCODER LAYERS
encoded1 = Dense(20, activation = 'relu')(input_dim)
encoded2 = Dense(10, activation = 'relu')(encoded1)
encoded3 = Dense(5, activation = 'relu')(encoded2)
encoded4 = Dense(encoding_dim, activation = 'relu')(encoded3)
# DEFINE THE DECODER LAYERS
decoded1 = Dense(5, activation = 'relu')(encoded4)
decoded2 = Dense(10, activation = 'relu')(decoded1)
decoded3 = Dense(20, activation = 'relu')(decoded2)
decoded4 = Dense(ncol, activation = 'sigmoid')(decoded3)
# COMBINE ENCODER AND DECODER INTO AN AUTOENCODER MODEL
autoencoder = Model(input = input_dim, output = decoded4)
# CONFIGURE AND TRAIN THE AUTOENCODER