== My Notes on MAE vs MSE Error Metrics
https://hackernoon.com/my-notes-on-mae-vs-mse-error-metrics


MAE:
- The idea behind the absolute error is to avoid mutual cancellation of the positive and negative errors.
- Absolute error has only non-negative values.
- By the same token, avoiding potential of mutual cancelations has its price — skewness (bias)cannot be determined. Absolute error preserves the same units of measurement as the data under analysis and gives allindividual errors same weights (as compared to squared error).
- This distance is easilyinterpretable and when aggregated over a dataset using an arithmetic mean has a meaning ofaverage error.
- The use of absolute value might present difficulties in gradient calculation of model parameters. This distance is used in such popular metrics as MAE, MdAE, etc.

MSE:
- Squared error follows the same idea as the absolute error — avoid negative error values and mutual cancellation of errors.
- Due to the square, large errors are emphasized and have relatively greater effect on the value of performance metric. At the same time, the effect of relatively small errors will be even smaller. Sometimes this property of the squared error is referred to as penalizing extreme errors or being susceptible to outliers. Based on the application, this property may be considered positive or negative. For example, emphasizing large errors may be desirable discriminating measure in evaluating models.
- In case of data outliers , MSE will become much larger compared to MAE. Avoiding potential of mutual cancelations has its price — skewness (bias)cannot be determined (for MAE).
- In MSE, error increases in a quadratic fashion while the error increases in a proportional fashion in MAE.
- In MSE since the error being squared, any prediction error is being heavily penalized.