Welcome to the next step in your journey through the "Time Series Forecasting with LSTMs" course. In this lesson, we will focus on evaluating LSTM models to understand their performance in time series forecasting tasks. As you may recall from previous lessons, LSTMs are powerful tools for capturing temporal dependencies in sequence data. However, to ensure that our models are effective, we need to evaluate their predictions accurately. This lesson will guide you through the process of assessing prediction accuracy using evaluation metrics and visualizing the results to gain insights into model performance.

The Root Mean Squared Error (RMSE) is calculated using the following formula:

where $y_i$ is the actual value, $\hat{y}_i$ is the predicted value, and $n$ is the number of observations.

The Mean Absolute Error (MAE) is calculated using the following formula:

where $y_i$ is the actual value, $\hat{y}_i$ is the predicted value, and $n$ is the number of observations.

The Mean Absolute Percentage Error (MAPE) is calculated using the following formula:

where $y_i$ is the actual value, $\hat{y}_i$ is the predicted value, and $n$ is the number of observations.

The R² Score (Coefficient of Determination) is calculated using the following formula:

where $y_i$ is the actual value, $\hat{y}_i$ is the predicted value, $\bar{y}$ is the mean of the actual values, and $n$ is the number of observations.

Let's walk through an example of predicting temperature using an LSTM model and evaluating its performance using RMSE, MAE, MAPE, and R² Score. Suppose we have already trained an LSTM model on temperature data. We can use this model to make predictions and then compute these metrics to evaluate its accuracy.

In this example, we first use the predict method of the trained LSTM model to generate predictions for the input data X. We then calculate the RMSE, MAE, MAPE, and R² Score using functions from the sklearn library and basic numpy operations. These metrics provide a comprehensive evaluation of the model's prediction accuracy, allowing you to assess its performance from different perspectives.

Visualizing the predictions of an LSTM model is an essential step in understanding its performance. By plotting the actual and predicted values, you can gain insights into how well the model captures the underlying patterns in the data. Visualization helps identify trends, discrepancies, and areas where the model may need improvement. Let's see how to create a plot to visualize the predictions.

In this example, we use the matplotlib library to create a plot of the actual and predicted temperature values. The plot function is used to draw lines representing the actual and predicted values, with different line styles for clarity. The legend function adds a legend to the plot, making it easy to distinguish between the actual and predicted values. By using different line styles and labels, the plot becomes more readable and informative, allowing you to easily compare the model's predictions with the actual values. By visualizing the predictions, you can assess the model's performance and identify any discrepancies between the predicted and actual values.

In this lesson, we explored the importance of evaluating LSTM models and visualizing their predictions. We covered the use of RMSE, MAE, MAPE, and R² Score as key evaluation metrics to assess prediction accuracy and demonstrated how to plot actual vs. predicted values using matplotlib. These techniques are essential for understanding model performance and identifying areas for improvement. As you move on to the practice exercises, I encourage you to apply these evaluation and visualization techniques to your own LSTM models. Experiment with different datasets and parameters to deepen your understanding and improve your forecasting skills. This hands-on practice will solidify the concepts covered in this lesson and prepare you for more advanced topics in the course.