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# 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
network.add(layers.Dense(units=32, activation='relu', input_shape=(train_features.shape[1],)))
# Add fully connected layer with a ReLU activation function
network.add(layers.Dense(units=32, activation='relu'))
# 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
```