Training and evaluation of an LSTM-based recurrent neural network (RNN) for stock price prediction are discussed. The model learns to predict future stock prices based on past data through a process that includes defining the architecture, configuring the loss function and optimizer, training the model, and evaluating its performance.

• Model definition: the LSTM model is defined using PyTorch, with key components such as the input size, hidden layer size, and the number of layers. The model consists of an LSTM layer followed by a linear layer for output prediction. The model is designed to take the previous stock prices as input and predict the next time step's price;

  class LSTMModel(nn.Module):
      def __init__(self, input_size=1, hidden_layer_size=50, num_layers=2, output_size=1):
          super().__init__()
          self.hidden_layer_size = hidden_layer_size
          self.num_layers = num_layers
          self.lstm = nn.LSTM(input_size, hidden_layer_size, num_layers, batch_first=True)
          self.linear = nn.Linear(hidden_layer_size, output_size)
  
      def forward(self, input_seq):
          h0 = torch.zeros(self.num_layers, input_seq.size(0), self.hidden_layer_size).to(input_seq.device)
          c0 = torch.zeros(self.num_layers, input_seq.size(0), self.hidden_layer_size).to(input_seq.device)
          lstm_out, _ = self.lstm(input_seq, (h0.detach(), c0.detach()))
          last_time_step_out = lstm_out[:, -1, :]
          predictions = self.linear(last_time_step_out)
          return predictions
  

• Training the model: in this step, the model is trained using the mean squared error (MSE) loss function and the adam optimizer. The model is trained over several epochs, with the loss computed and updated for each batch of training data. The training loop includes forward and backward propagation, optimizing the weights to minimize the loss. During training, we monitor the loss value to ensure the model is learning effectively;

  criterion = nn.MSELoss()
  optimizer = optim.Adam(model.parameters(), lr=0.001)
  

• Evaluation: after training, the model is evaluated on the test dataset. The model's predictions are compared against the actual stock prices using root mean squared error (RMSE) as the evaluation metric. This metric measures the difference between the predicted and actual values, with a lower RMSE indicating better performance. The evaluation process also includes inverse transforming the scaled predictions to get the actual price values for comparison;

• Performance metric: the RMSE is used to assess how well the model performs on unseen data. A lower RMSE value indicates that the model's predictions are closer to the actual values. The RMSE is calculated after comparing the predicted values with the actual unscaled values from the test data.

In summary, this chapter outlines the process of training and evaluating an LSTM model for time series forecasting, with a focus on stock price prediction. Key steps include model definition, training using the MSE loss function and Adam optimizer, and evaluating the model using RMSE.