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'))