Chapter 11 Neural Networks

An illustration of a single neuron.

Figure 11.1: An illustration of a single neuron.

An illustration of three activation functions: Sigmoid (left panel), Tanh (middle panel), and ReLU (right panel).An illustration of three activation functions: Sigmoid (left panel), Tanh (middle panel), and ReLU (right panel).An illustration of three activation functions: Sigmoid (left panel), Tanh (middle panel), and ReLU (right panel).

Figure 11.2: An illustration of three activation functions: Sigmoid (left panel), Tanh (middle panel), and ReLU (right panel).

Top: a neural network with one hidden layer.Bottom: coefficients of a neural network with one hidden layer.

Figure 11.3: Bottom: coefficients of a neural network with one hidden layer.

A neural network with three hidden layers.

Figure 11.4: A neural network with three hidden layers.

A neural network with one hidden layer.

Figure 11.5: A neural network with one hidden layer.

A neural network with one hidden layer.

Figure 11.6: A neural network with one hidden layer.

Daily new deaths for Florida. Top: two weeks ahead forecast using nnetar.Center: two weeks ahead forecast using nnetar with predictions constrained to positive values.Bottom: two weeks ahead forecast and prediction intervals using nnetar with predictions constrained to positive values.

Figure 11.7: Bottom: two weeks ahead forecast and prediction intervals using nnetar with predictions constrained to positive values.

An example of neural network with one hidden layer.

Figure 11.8: An example of neural network with one hidden layer.