Mean absolute percentage error

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Mean Absolute Percentage Error (MAPE) is a simple way to measure forecast accuracy.

How it works
- For each point i, calculate the absolute error as a percentage of the actual value: |Forecast_i − Actual_i| / |Actual_i|.
- Average these percentage errors over all points: MAPEs = (1/n) × sum of those values.
- The result is expressed as a percent.

Cautions
- MAPE can be misleading when actual values are very small, because tiny numbers can inflate the percentage error.

Weighted version: wMAPE
- To reduce the distortion from small actuals, a weighted version is often used.
- A common form is wMAPE = sum |Actual_i − Forecast_i| / sum |Actual_i|.
- Sometimes people refer to a “double-weighted” version (wwMAPE) where another set of weights is applied to both numerator and denominator.

MAPE in regression
- MAPE can also be used as a loss function in regression.
- It is equivalent to a weighted absolute error: minimizing the sum of weights × |Forecast_i − Actual_i| with weights equal to 1/|Actual_i|.
- In practice, this means you can fit models using weighted MAE or quantile regression techniques.

Practical notes
- MAPE is intuitive and easy to interpret, but it has important drawbacks.
- Because of its sensitivity to small actuals, many practitioners prefer alternatives like wMAPE or other error measures.

Other variants
- There are several related measures and variants designed to address the weaknesses of MAPE; researchers continue to propose alternatives.