Mean Absolute Error (MAE) Measure
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A Mean Absolute Error (MAE) Measure is an approximation error measure based on the mean of the absolute errors (over all predicted values).
- AKA: Absolute Average Deviation.
- Context:
- It weighs the distance between the prediction and observation equally regardless of the distance to the critical operating points.
- It is commonly used to measure forecast error in time series analysis.
- …
- Counter-Example(s):
- See: Estimator Evaluation Metric, Absolute Deviation, Median Absolute Deviation, Estimation Model Error Estimator.
References
2013
- (Wikipedia - MAE, 2013) ⇒ http://en.wikipedia.org/wiki/Mean_absolute_error
- QUOTE: In statistics, the mean absolute error (MAE) is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by :[math]\displaystyle{ \mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \left| f_i-y_i\right| =\frac{1}{n}\sum_{i=1}^n \left| e_i \right|. }[/math] As the name suggests, the mean absolute error is an average of the absolute errors [math]\displaystyle{ e_i = |f_i - y_i| }[/math], where [math]\displaystyle{ f_i }[/math] is the prediction and [math]\displaystyle{ y_i }[/math] the true value. Note that alternative formulations may include relative frequencies as weight factors.
The mean absolute error is a common measure of forecast error in time series analysis, where the terms "mean absolute deviation" is sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally.
- QUOTE: In statistics, the mean absolute error (MAE) is a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by :[math]\displaystyle{ \mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \left| f_i-y_i\right| =\frac{1}{n}\sum_{i=1}^n \left| e_i \right|. }[/math] As the name suggests, the mean absolute error is an average of the absolute errors [math]\displaystyle{ e_i = |f_i - y_i| }[/math], where [math]\displaystyle{ f_i }[/math] is the prediction and [math]\displaystyle{ y_i }[/math] the true value. Note that alternative formulations may include relative frequencies as weight factors.
2011
- (Sammut & Webb, 2011) ⇒ Claude Sammut, and Geoffrey I. Webb. (2011). “Mean Absolute Error.” In: (Sammut & Webb, 2011). p.652.
- QUOTE: Mean Absolute Error is a model evaluation metric used with regression models. The mean absolute error of a model with respect to a test set is the mean of the absolute values of the individual prediction errors on over all instances in the test set. Each prediction error is the difference between the true value and the predicted value for the instance. : [math]\displaystyle{ mae=\frac{∑^n_{i=1}abs(y_i−λ(x_i))}{n} }[/math] where y_i is the true target value for test instance x_i, λ(x_i) is the predicted target value for test instance x_i, and n is the number of test instances.