Mean absolute error
Encyclopedia
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
As the name suggests, the mean absolute error is an average of the absolute errors
, where 
is the prediction and 
the true value. Note that alternative formulations may include relative frequencies as weight factors.
T
The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the mean absolute scaled error
(MASE) and the mean squared error
. These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the mean signed difference.
Where a prediction model is to be fitted using a selected performance measure, in the sense that the least squares
approach is related to the mean squared error
, the equivalent for mean absolute error is least absolute deviations
.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, 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
As the name suggests, the mean absolute error is an average of the absolute errors
, where is the prediction and the true value. Note that alternative formulations may include relative frequencies as weight factors.T
The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the mean absolute scaled error
Mean absolute scaled error
In statistics, the mean absolute scaled error is a measure of the accuracy of forecasts . It was proposed in 2006 by Australian statistician Rob Hyndman, who described it as a "generally applicable measurement of forecast accuracy without the problems seen in the other measurements."The mean...
(MASE) and the mean squared error
Mean squared error
In statistics, the mean squared error of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or...
. These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the mean signed difference.
Where a prediction model is to be fitted using a selected performance measure, in the sense that the least squares
Least squares
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
approach is related to the mean squared error
Mean squared error
In statistics, the mean squared error of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or...
, the equivalent for mean absolute error is least absolute deviations
Least absolute deviations
Least absolute deviations , also known as Least Absolute Errors , Least Absolute Value , or the L1 norm problem, is a mathematical optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data...
.