# Feedforward Neural Networks For Regression

## Preliminaries

# Load libraries
import numpy as np
from keras.preprocessing.text import Tokenizer
from keras import models
from keras import layers
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn import preprocessing

# Set random seed
np.random.seed(0)
Using TensorFlow backend.


## Generate Training Data

# Generate features matrix and target vector
features, target = make_regression(n_samples = 10000,
n_features = 3,
n_informative = 3,
n_targets = 1,
noise = 0.0,
random_state = 0)

# Divide our data into training and test sets
train_features, test_features, train_target, test_target = train_test_split(features,
target,
test_size=0.33,
random_state=0)

## Create Neural Network Architecture

# Start neural network
network = models.Sequential()

# Add fully connected layer with a ReLU activation function

# Add fully connected layer with a ReLU activation function

# Add fully connected layer with no activation function
network.add(layers.Dense(units=1))

## Compile Neural Network

Because we are training a regression, we should use an appropriate loss function and evaluation metric, in our case the mean square error:

$$\operatorname {MSE}={\frac {1}{n}}\sum_{{i=1}}^{n}({\hat {y_{i}}}-y_{i})^{2}$$

where $n$ is the number of observations, $y_{i}$ is the true value of the target we are trying to predict, $y$, for observation $i$, and ${\hat {y_{i}}}$ is the model’s predicted value for $y_{i}$.

# Compile neural network
network.compile(loss='mse', # Mean squared error
optimizer='RMSprop', # Optimization algorithm
metrics=['mse']) # Mean squared error

## Train Neural Network

# Train neural network
history = network.fit(train_features, # Features
train_target, # Target vector
epochs=10, # Number of epochs
verbose=0, # No output
batch_size=100, # Number of observations per batch
validation_data=(test_features, test_target)) # Data for evaluation