One common task in Data Science is solving regression problems. Several metrics are available to choose from when evaluating the performance of regression models. The most standard ones are Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). Each of these metrics has strengths and weaknesses; choosing the right one depends on the problem and context. But what do they mean, and how do they differ?
In this blog post, I will explain the meaning and intuition behind these metrics and provide some guidance on when to use which one.
MAE is the most straightforward and intuitive metric among the three. It is calculated by taking the average of the absolute values of the errors, which are the differences between the predicted and actual values. For example, if you have a dataset with five observations and your model predicts [12, 13, 14, 15, 16] while the actual values are [10, 11, 12, 13, 14], then the MAE is (|10-12| + |11-13| + |12-14| + |13-15| + |14-16|) / 5 = 2. MAE measures how close the predictions are to the actual values on average, regardless of the direction of the error. It is advantageous when the outliers in the dataset can significantly impact the model's performance. This is because MAE is less sensitive to outliers than MSE or RMSE. In addition, because MAE is calculated based on absolute differences, it measures how far off the predictions are on average, which can help interpret the model's performance.
The MAE has some nice properties:
However, the MAE also has some drawbacks:
MSE stands for Mean Squared Error, and it is calculated as the average of the squared differences between the actual and predicted values. Using the same example as above, the MSE is ((10-12)^2 + (11-13)^2 + (12-14)^2 + (13-15)^2 + (14-16)^2) / 5 = 4. MSE measures how close the predictions are to the actual values on average, but it gives more weight to large errors than small ones. This means that MSE is more sensitive to outliers and can be useful in identifying models that make large mistakes.
The MSE has some advantages over the MAE:
However, the MSE also has some disadvantages:
RMSE stands for Root Mean Squared Error, and it is calculated as the square root of the MSE. Using the same example above, the RMSE is sqrt(MSE) = sqrt(4) = 2. RMSE has the same unit as the actual and predicted values, making comparing them easier. RMSE also measures how close the predictions are to the true values on average, but it gives more weight to large errors than small ones. RMSE is one of the most common metrics in regression because it is easy to differentiate and use with gradient-based methods.
The RMSE has some benefits over both MAE and MSE:
However, the RMSE also has some drawbacks:
So, how do you choose between MAE, MSE and RMSE? There is no definitive answer to which metric to use for regression problems. It depends on your data, your model and your objective. Here are some general guidelines: